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In \cite{Ha86} Harer explicitly constructed a spine for the decorated Teichm\"uller space of orientable surfaces with at least one puncture and negative Euler characteristic. In this paper we point out some instances where his computation of the dimension of this spine is off by $1$ and give the correct dimension., Comment: 10 pages, 4 figures

Unraveling the nature of dark matter (DM) stands as a primary objective in modern physics. Here we present evidence suggesting deviations from the collisionless Cold DM (CDM) paradigm. It arises from the radial distribution of stars in six Ultra Faint Dwarf (UFD) galaxies measured with the Hubble Space Telescope (HST). After a trivial renormalization in size and central density, the six UFDs show the same stellar distribution, which happens to have a central plateau or core. Assuming spherical symmetry and isotropic velocities, the Eddington inversion method proves the observed distribution to be inconsistent with potentials characteristic of CDM particles. Under such assumptions, the observed innermost slope of the stellar profile discards the UFDs to reside in a CDM potential at a > 97% confidence level. The extremely low stellar mass of these galaxies, 10**3-10**4 Msun , prevents stellar feedback from modifying the shape of a CDM potential. Other conceivable explanations for the observed cores, like deviations from spherical symmetry and isotropy, tidal forces, and the exact form of the used CDM potential, are disfavored by simulations and/or observations. Thus, the evidence suggests that collisions among DM particles or other alternatives to CDM are likely shaping these galaxies. Many of these alternatives produce cored gravitational potentials, shown here to be consistent with the observed stellar distribution., Comment: Accepted for publication in The Astrophysical Journal Letters (ApJL)

*** Context: The halos of low-mass galaxies may allow us to constrain the nature of dark matter (DM), but the kinematic measurements to diagnose the required properties are technically extremely challenging. However, the photometry of these systems is doable. Aims. Using only stellar photometry, constrain key properties of the DM haloes in low-mass galaxies. *** Methods: Unphysical pairs of DM gravitational potentials and starlight distributions can be identified if the pair requires a distribution function f that is negative somewhere in the phase space. We use the classical Eddington inversion method (EIM) to compute f for a battery of DM gravitational potentials and around 100 observed low-mass galaxies with Mstar between 10**6 and 10**8 Msun. The battery includes NFW potentials (expected from cold DM) and potentials stemming from cored mass distributions (expected in many alternatives to cold DM). The method assumes spherical symmetry and isotropic velocity distribution and requires fitting the observed profiles with analytic functions, for which we use polytropes (with zero inner slope, a.k.a. core) and profiles with variable inner and outer slopes. The validity of all these assumptions is analyzed. *** Results: In general, the polytropes fit well the observed starlight profiles. If they were the correct fits (which could be the case) then all galaxies are inconsistent with NFW-like potentials. Alternatively, when the inner slope is allowed to vary for fitting, between 40% and 70% of the galaxies are consistent with cores in the stellar mass distribution and thus inconsistent with NFW-like potentials. *** Conclusions: Even though the stellar mass of the observed galaxies is still not low enough to constrain the nature of DM, this work shows the practical feasibility of the EIM technique to infer DM properties only from photometry., Comment: Accepted for publication in A&A

It was known that an ideal spherically symmetric stellar system with isotropic velocities and an inner core cannot reside in a Navarro, Frenk, and White (NFW) gravitational potential. The incompatibility can be pinned down to the radial gradient of the NFW potential in the very center of the system, which differs from zero. The gradient is identically zero in an Einasto potential, also an alternative representation of the dark matter (DM) halos created by the kind of cold DM (CDM) defining the current cosmological model. Here we show that, despite the inner gradient being zero, stellar cores are also inconsistent with Einasto potentials. This result may have implications to constrain the nature of DM through interpreting the stellar cores often observed in dwarf galaxies., Comment: RNAAS complementing our previous paper Sanchez Almeida et al. (2023, ApJ, 954, 153; doi: 10.3847/1538-4357/ace534)

A long linear structure recently discovered could be the stellar wake produced by the passage of a runaway supermassive black hole (SMBH) or, alternatively, a bulgeless edge-on galaxy. We report on new very deep HST imaging that seems to be in tension with the SMBH runaway scenario but is consistent with the bulgeless edge-on galaxy scenario. The new observations were aimed at detecting two key features expected in the SMBH scenario, namely, the bow shock formed where the SMBH meets the surrounding medium, and a counter stellar wake created by another binary SMBH hypothesized as part of the ejection mechanism. Neither of these two features appears to be present in the new images, as would be expected in the edge-on galaxy scenario., Comment: Accepted for publication in RNAAS

We provide an explicit computation of the cohomology groups (with untwisted coefficients) of semidirect products of the form $\mathbb{Z}^n\rtimes \mathbb{Z}/m$ with $m$ free of squares, by means of formulas that only depend on $n$, $m$ and the action of $\mathbb{Z}/m$ on $\mathbb{Z}^n$. We want to highlight the fact that we are not impossing any conditions on the $\mathbb{Z}/m$-action on $\mathbb{Z}^n$, and as far as we know our formulas are the first in the literature in this generality. This generalizes previous computations of L\"uck-Davis and Adem-Ge-Pan-Petrosyan. In order to show that our formulas are usable, we develop a concrete example of the form $\mathbb{Z}^5\rtimes \mathbb{Z}/6$ where its cohomology groups are described in full detail.

Context. One of the most fundamental scaling relations in galaxies is observed between metallicity and stellar mass -- the mass-metallicity relation (MZR) -- although recently a stronger dependence of the gas-phase metallicity with the galactic gravitational potential ($\Phi \rm ZR$) has been reported. Further dependences of metallicity on other galaxy properties have been revealed, with the star formation rate (SFR) being one of the most studied and debated secondary parameters in the relation (the so-called fundamental metallicity relation). Aims. In this work we explore the dependence of the gas-phase metallicity residuals from the MZR and $\Phi \rm ZR$ on different galaxy properties in the search for the most fundamental scaling relation in galaxies. Methods. We applied a random forest regressor algorithm on a sample of 3430 nearby star-forming galaxies from the SDSS-IV MaNGA survey. Using this technique, we explored the effect of 147 additional parameters on the global oxygen abundance residuals obtained after subtracting the MZR. Alternatively, we followed a similar approach with the metallicity residuals from the $\Phi \rm ZR$. Results. The stellar metallicity of the galaxy is revealed as the secondary parameter in both the MZR and the $\Phi \rm ZR$, ahead of the SFR. This parameter reduces the scatter in the relations $\sim 10-15\%$. We find the 3D relation between gravitational potential, gas metallicity, and stellar metallicity to be the most fundamental metallicity relation observed in galaxies., Comment: 8 pages, 5 figures, accepted for publication in A&A Letters

Interpreting the scaling relations followed by galaxies is a fundamental tool for assessing how well we understand galaxy formation and evolution. Several scaling relations involving the galaxy metallicity have been discovered through the years, the foremost of which is the scaling with stellar mass. This so-called mass-metallicity relation is thought to be fundamental and has been subject to many studies in the literature. We study the dependence of the gas-phase metallicity on many different galaxy properties to assess which of them determines the metallicity of a galaxy. We applied a random forest regressor algorithm on a sample of more than 3000 nearby galaxies from the SDSS-IV MaNGA survey. Using this machine-learning technique, we explored the effect of 148 parameters on the global oxygen abundance as an indicator of the gas metallicity. $M_{\rm \star}$/$R_e$, as a proxy for the baryonic gravitational potential of the galaxy, is found to be the primary factor determining the average gas-phase metallicity of the galaxy ($Z_g$). It outweighs stellar mass. A subsequent analysis provides the strongest dependence of $Z_g$ on $M_\star / R_e^{\,0.6}$. We argue that this parameter traces the total gravitational potential, and the exponent $\alpha\simeq 0.6$ accounts for the inclusion of the dark matter component. Our results reveal the importance of the relation between the total gravitational potential of the galaxy and the gas metallicity. This relation is tighter and likely more primordial than the widely known mass-metallicity relation., Comment: Accepted for publication in A&A

We prove that the virtually cyclic (geometric) dimension of the finite index congruence subgroup $\mathrm{IA}_N(3)$ of $\mathrm{Out}(F_N)$ is $2N-2$. From this we deduce the virtually cyclic dimension of $\mathrm{Out}(F_N)$ is finite. Along the way we prove L\"uck's property (C) holds for $\mathrm{Out}(F_N)$, we prove that the commensurator of a cyclic subgroup of $\mathrm{IA}_N(3)$ equals its centraliser, we give an $\mathrm{IA}_N(3)$ analogue of various exact sequences arising from reduction systems for mapping class groups, and give a near complete description of centralisers of infinite order elements in $\mathrm{IA}_3(3)$., Comment: 35 pages, comments welcome

For a topological group $G$ let $E_{\textsf{com}}(G)$ be the total space of the universal transitionally commutative principal $G$-bundle as defined by Adem--Cohen--Torres-Giese. So far this space has been most studied in the case of compact Lie groups; but in this paper we focus on the case of infinite discrete groups. For a discrete group $G$, the space $E_{\textsf{com}}(G)$ is homotopy equivalent to the geometric realization of the order complex of the poset of cosets of abelian subgroups of $G$. We show that for fundamental groups of closed orientable geometric $3$-manifolds, this space is always homotopy equivalent to a wedge of circles. On our way to prove this result we also establish some structural results on the homotopy type of $E_{\textsf{com}}(G)$., Comment: 36 pages, 4 figures, comments very welcome!

According to the current concordance cosmological model, the dark matter (DM) particles are collision-less and produce self-gravitating structures with a central cusp which, generally, is not observed. The observed density tends to a central plateau or core, explained within the cosmological model through the gravitational feedback of baryons on DM. This mechanism becomes inefficient when decreasing the galaxy stellar mass so that in the low-mass regime (Mstar << 10**6 Msun) the energy provided by the baryons is insufficient to modify cusps into cores. Thus, if cores exist in these galaxies they have to reflect departures from the collision-less nature of DM. Measuring the DM mass distribution in these faint galaxies is extremely challenging, however, their stellar mass distribution can be characterized through deep photometry. Here we provide a way of using only the stellar mass distribution to constrain the underlying DM distribution. The so-called Eddington inversion method allows us to discard pairs of stellar distributions and DM potentials requiring (unphysical) negative distribution functions in the phase space. In particular, cored stellar density profiles are incompatible with the Navarro, Frenk, and White (NFW) potential expected from collision-less DM if the velocity distribution is isotropic and the system spherically symmetric. Through a case-by-case analysis, we are able to relax these assumptions to consider anisotropic velocity distributions and systems which do not have exact cores. In general, stellar distributions with radially biased orbits are difficult to reconcile with NFW-like potentials, and cores in the baryon distribution tend to require cores in the DM distribution., Comment: Accepted for publication in ApJ

van Dokkum et al. (2023) reported the serendipitous discovery of a thin linear object interpreted as the trail of star-forming regions left behind by a runaway supermassive black hole (SMBH) kicked out from the center of a galaxy. Despite the undeniable interest in the idea, the actual physical interpretation is not devoid of difficulty. The wake of a SMBH produces only small perturbations on the external medium, which has to be in exceptional physical conditions to collapse gravitationally and form a long (40 kpc) massive (3e9 Msun) stellar trace in only 39 Myr. Here we offer a more conventional explanation: the stellar trail is a bulgeless galaxy viewed edge-on. This interpretation is supported by the fact that its position--velocity curve resembles a rotation curve which, together with its stellar mass, puts the object right on top of the Tully-Fisher relation characteristic of disk galaxies. Moreover, the rotation curve (Vmax sim 110 km/s), stellar mass, extension, width (z0 sim 1.2 kpc), and surface brightness profile of the object are very much like those of IC5249, a well-known local bulgeless edge-on galaxy. These observational facts are difficult to interpret within the SMBH wake scenario. We discuss in detail the pros and cons of the two options., Comment: Accepted for publication in A&A Letters

Let $\mathrm{Mod}(S)$ be the mapping class group of a compact connected orientable surface $S$, possibly with punctures and boundary components, with negative Euler characteristic. We prove that for any infinite virtually abelian subgroup $H$ of $\mathrm{Mod}(S)$, there is a subgroup $H'$ commensurable with $H$ such that the commensurator of $H$ equals the normalizer of $H'$. As a consequence we give, for each $n \geq 2$, an upper bound for the geometric dimension of $\mathrm{Mod}(S)$ for the family of abelian subgroups of rank bounded by $n$. These results generalize work by Juan-Pineda--Trujillo-Negrete and Nucinkis--Petrosyan for the virtually cyclic case., Comment: 19 pages, 1 figure

Tadpole galaxies are metal-poor dwarfs with typically one dominant star-forming region, giving them a head-tail structure when inclined. A metallicity drop in the head suggests that gas accretion with even lower metallicity stimulated the star formation. Here we present multiband HST WFC3 and ACS images of four nearby (<25 Mpc) tadpoles, SBS0, SBS1, Kiso 3867, and UM461, selected for their clear metallicity drops shown in previous spectroscopic studies. Properties of the star complexes and compact clusters are measured. Each galaxy contains from 3 to 10 young stellar complexes with 10^3-10^5 Msun of stars ~3-10 Myr old. Between the complexes, the disk has a typical age of ~3 Gyr. Numerous star clusters cover the galaxies, both inside and outside the complexes. The combined cluster mass function, made by normalizing the masses and counts before stacking, is a power law with a slope of -1.12+-0.14 on a log-log plot and the combined distribution function of cluster lifetime decays with age as t^{-0.65+-0.24}. A comparison between the summed theoretical Lyman continuum (LyC) emission from all the clusters, given their masses and ages, is comparable to or exceeds the LyC needed to excite the observed Halpha in some galaxies, suggesting LyC absorption by dust or undetected gas in the halo, or perhaps galaxy escape., Comment: 20 pages, 16 figures, accepted by ApJ

This survey studies pairs $(G,\mathcal{P})$ with $G$ a finitely generated group and $\mathcal{P}$ a (finite) collection of subgroups of $G$. We explore the notion of quasi-isometry of such pairs and the notion of a qi-characteristic collection of subgroups. Both notions are abstractions of phenomena that have appeared repeatedly in the work of several people within the quasi-isometric rigidity realm., Comment: 14 pages

For a finitely generated group $G$, let $H(G)$ denote Bowditch's taut loop length spectrum. We prove that if $G=(A\ast B) / \langle\!\langle \mathcal R \rangle\!\rangle $ is a $C'(1/12)$ small cancellation quotient of a the free product of finitely generated groups, then $H(G)$ is equivalent to $H(A) \cup H(B)$. We use this result together with bounds for cohomological and geometric dimensions, as well as Bowditch's construction of continuously many non-quasi-isometric $C'(1/6)$ small cancellation $2$-generated groups to obtain our main result: Let $\mathcal{G}$ denote the class of finitely generated groups. The following subclasses contain continuously many one-ended non-quasi-isometric groups: $\bullet\left\{G\in \mathcal{G} \colon \underline{\mathrm{cd}}(G) = 2 \text{ and } \underline{\mathrm{gd}}(G) = 3 \right\}$ $\bullet\left\{G\in \mathcal{G} \colon \underline{\underline{\mathrm{cd}}}(G) = 2 \text{ and } \underline{\underline{\mathrm{gd}}}(G) = 3 \right\}$ $\bullet\left\{G\in \mathcal{G} \colon \mathrm{cd}_{\mathbb{Q}}(G)=2 \text{ and } \mathrm{cd}_{\mathbb{Z}}(G)=3 \right\}$ On our way to proving the aforementioned results, we show that the classes defined above are closed under taking relatively finitely presented $C'(1/12)$ small cancellation quotients of free products, in particular, this produces new examples of groups exhibiting an Eilenberg-Ganea phenomenon for families. We also show that if there is a finitely presented counter-example to the Eilenberg-Ganea conjecture, then there are continuously many finitely generated one-ended non-quasi-isometric counter-examples., Comment: 21 pages

For a finitely generated group $G$ and collection of subgroups $\mathcal{P}$ we prove that the relative Dehn function of a pair $(G,\mathcal{P})$ is invariant under quasi-isometry of pairs. Along the way we show quasi-isometries of pairs preserve almost malnormality of the collection and fineness of the associated coned off Cayley graphs. We also prove that for a cocompact simply connected combinatorial $G$-$2$-complex $X$ with finite edge stabilisers, the combinatorial Dehn function is well-defined if and only if the $1$-skeleton of $X$ is fine. We also show that if $H$ is a hyperbolically embedded subgroup of a finitely presented group $G$, then the relative Dehn function of the pair $(G, H)$ is well-defined. In the appendix, it is shown that show that the Baumslag-Solitar group $\mathrm{BS}(k,l)$ has a well-defined Dehn function with respect to the cyclic subgroup generated by the stable letter if and only if neither $k$ divides $l$ nor $l$ divides $k$., Comment: Appendix by Ashot Minasyan

We present a new measurement of the gas-phase mass-metallicity relation (MZR), and its dependence on star formation rates (SFRs) at 1.3 < z < 2.3. Our sample comprises 1056 galaxies with a mean redshift of z = 1.9, identified from the Hubble Space Telescope Wide Field Camera 3 (WFC3) grism spectroscopy in the Cosmic Assembly Near-Infrared Deep Extragalactic Survey (CANDELS) and the WFC3 Infrared Spectroscopic Parallel Survey (WISP). This sample is four times larger than previous metallicity surveys at z ~ 2, and reaches an order of magnitude lower in stellar mass (10^8 M_sun). Using stacked spectra, we find that the MZR evolves by 0.3 dex relative to z ~ 0.1. Additionally, we identify a subset of 49 galaxies with high signal-to-noise (SNR) spectra and redshifts between 1.3 < z < 1.5, where H-alpha emission is observed along with [OIII] and [OII]. With accurate measurements of SFR in these objects, we confirm the existence of a mass-metallicity-SFR (M-Z-SFR) relation at high redshifts. These galaxies show systematic differences from the local M-Z-SFR relation, which vary depending on the adopted measurement of the local relation. However, it remains difficult to ascertain whether these differences could be due to redshift evolution, as the local M-Z-SFR relation is poorly constrained at the masses and SFRs of our sample. Lastly, we reproduced our sample selection in the IllustrisTNG hydrodynamical simulation, demonstrating that our line flux limit lowers the normalization of the simulated MZR by 0.2 dex. We show that the M-Z-SFR relation in IllustrisTNG has an SFR dependence that is too steep by a factor of around three., Comment: Accepted for publication in ApJ; 41 pages, 20 figures

For a group $G$, let $\mathcal{F}_{n}$ be the family of all the subgroups of $G$ containing a subgroup isomorphic to $\mathbb{Z}^{r}$ for some $r=0,1,2,\dots ,n$ of finite index. Joecken, Lafont and S\'anchez Salda\~na computed the $\mathcal{F}_1$-dimension of 3-manifold groups. The goal of this article is to compute the $\mathcal{F}_n$-geometric dimension of 3-manifold groups for all $n\geq 2$., Comment: 22 pages, 1 table. Proofs of Theorem 3.1, Theorem 4.5 c), and Proposition 5.1 were expanded for the sake of clarity. Title was changed

Self-gravitating astronomical objects often show a central plateau in the density profile (core) whose physical origin is hotly debated. Cores are theoretically expected in N-body systems of maximum entropy, however, they are not present in the canonical N-body numerical simulations of cold dark matter (CDM). Our work shows that despite this apparent contradiction between theory and numerical simulations, they are fully consistent. Simply put, cores are characteristic of systems in thermodynamic equilibrium, but thermalizing collisions are purposely suppressed in CDM simulations. When collisions are allowed, N-body numerical simulations develop cored density profiles, in perfect agreement with the theoretical expectation. We compare theory and two types of numerical simulations: (1) when DM particles are self-interacting (SIDM) with enough cross-section, then the effective two-body relaxation timescale becomes shorter than the Hubble time resulting in cored DM haloes. The haloes thus obtained, with masses from dwarf galaxies to galaxy clusters, collapse to a single shape after normalization, and this shape agrees with the polytropic density profile theoretically expected. (2) The inner radii in canonical N-body numerical simulations are always discarded because the use of finite-mass DM particles artificially increases the two-body collision rate. We show that the discarded radii develop cores that are larger than the employed numerical softening and have polytropic shapes independently of halo mass. Our work suggests that the presence of cores in simulated (or observed) density profiles can used as evidence for systems in thermodynamic equilibrium., Comment: Accepted for publications in MNRAS. 6 figures, 9 pages. Paper that complements arXiv:2009.08994

Let $G$ and $H$ be quasi-isometric finitely generated groups and let $P\leq G$; is there a subgroup $Q$ (or a collection of subgroups) of $H$ whose left cosets coarsely reflect the geometry of the left cosets of $P$ in $G$? We explore sufficient conditions for a positive answer. The article consider pairs of the form $(G,\mathcal{P})$ where $G$ is a finitely generated group and $\mathcal{P}$ a finite collection of subgroups, there is a notion of quasi-isometry of pairs, and quasi-isometrically characteristic collection of subgroups. A subgroup is qi-characteristic if it belongs to a qi-characteristic collection. Distinct classes of qi-characteristic collections of subgroups have been studied in the literature on quasi-isometric rigidity, we list in the article some of them and provide other examples. The first part of the article proves: if $G$ and $H$ are finitely generated quasi-isometric groups and $\mathcal{P}$ is a qi-characteristic collection of subgroups of $G$, then there is a collection of subgroups $\mathcal{Q}$ of $H$ such that $ (G, \mathcal{P})$ and $(H, \mathcal{Q})$ are quasi-isometric pairs. The second part of the article studies the number of filtered ends $\tilde e (G, P)$ of a pair of groups, a notion introduced by Bowditch, and provides an application of our main result: if $G$ and $H$ are quasi-isometric groups and $P\leq G$ is qi-characterstic, then there is $Q\leq H$ such that $\tilde e (G, P) = \tilde e (H, Q)$., Comment: Version 3. 25 pages. Updated list of references. Version accepted for publication in AGT

While all models for the evolution of galaxies require the accretion of gas to sustain their growth via on-going star formation, it has proven difficult to directly detect this inflowing material. In this paper we use data of nearby star-forming galaxies in the SDSS IV Mapping Nearby Galaxies at Apache Point Observatory (MaNGA) survey to search for evidence of accretion imprinted in the chemical composition of the interstellar medium. We measure both the O/H and N/O abundance ratios in regions previously identified as having anomalously low values of O/H. We show that the unusual locations of these regions in the N/O vs. O/H plane indicate that they have been created through the mixing of disk gas having higher metallicity with accreted gas having lower metallicity. Taken together with previous analysis on these anomalously low-metallicity regions, these results imply that accretion of metal-poor gas can probably sustain star formation in present-day late-type galaxies., Comment: 13 pages, 8 figures, accepted for publication in The Astrophysical Journal

We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The main tools we use are: the K-theoretic Farrell-Jones isomorphism conjecture, the construction of models for the universal space for the family of virtually cyclic subgroups in 3-manifold groups, and both the prime and JSJ-decompositions together with the well-known geometrization theorem., Comment: 21 pages

The search for new global scaling relations linking physical properties of galaxies has a fundamental interest. Furthermore, their recovery from spatially resolved relations has been one of the spotlights of integral field spectroscopy (IFS). In this study we investigate the existence of global and local relations between stellar age ($Age_\star$) and gas-phase metallicity ($Z_g$). To this aim, we analyze IFS data for a sample of 736 star-forming disk galaxies from the MaNGA survey. We report a positive correlation between the global $Z_g$ and $D(4000)$ (an indicator of stellar age), with a slope that decreases with increasing galaxy mass. Locally, a similar trend is found when analyzing the $Z_g$ and $D(4000)$ of the star-forming regions, as well as the residuals resulting from removing the radial gradients of both parameters. The local laws have systematically smaller slopes than the global one. We ascribe this difference to random errors, that make the true slope of the $Age_\star-Z_g$ relation to be systematically underestimated when performing a least square fitting. The explored relation is intimately linked with the already known relation between gas metallicity and star formation rate at fixed mass, both presenting a common physical origin., Comment: 16 pages, 7 figures. Accepted for publication in ApJ

Cold Dark Matter (CDM) simulations predict a central cusp in the mass distribution of galaxies. This prediction is in stark contrast with observations of dwarf galaxies which show a central plateau or 'core' in their density distribution. The proposed solutions to this core-cusp problem can be classified into two types. Either they invoke feedback mechanisms produced by the baryonic component of the galaxies, or they assume the properties of the dark matter (DM) particle to depart from the CDM hypothesis. Here we propose an alternative yet complementary explanation. We argue that cores are unavoidable in the self-gravitating systems of maximum entropy resulting from non-extensive statistical mechanics. Their structure follows from the Tsallis entropy, suitable for systems with long-range interactions. Strikingly, the mass density profiles predicted by such thermodynamic equilibrium match the observed cores without any adjustment or tuning. Thus, the principle of maximum Tsallis entropy explains the presence of cores in dwarf galaxies., Comment: Accepted for publication in A&A Letters. 3 pages, 2 figures

Let $\mathcal{N}_g$ be the mapping class group of a non-orientable closed surface. We prove that the proper cohomological dimension, the proper geometric dimension, and the virtual cohomological dimension of $\mathcal{N}_g$ are equal whenever $g\neq 4,5$. In particular, there exists a model for the classifying space of $\mathcal{N}_g$ for proper actions of dimension $\mathrm{vcd}(\mathcal{N}_g)=2g-5$. Similar results are obtained for the mapping class group of a non-orientable surface with boundaries and possibly punctures, and for the pure mapping class group of a non-orientable surface with punctures and without boundaries., Comment: 20 pages. Version accepted for publication in Homology, Homotopy and Applications

MAAT is proposed as a visitor mirror-slicer optical system that will allow the OSIRIS spectrograph on the 10.4-m Gran telescopio CANARIAS (GTC) the capability to perform Integral Field Spectroscopy (IFS) over a seeing-limited FoV 14.20''x10'' with a slice width of 0.303''. MAAT@GTC will enhance the resolution power of OSIRIS by 1.6 times as compared to its 0.6'' wide long-slit. All the eleven OSIRIS grisms and volume-phase holographic gratings will be available to provide broad spectral coverage with moderate resolution (R=600 up to 4100) in the 3600 - 10000 {\AA} wavelength range. MAAT unique observing capabilities will broaden its use to the needs of the GTC community to unveil the nature of most striking phenomena in the universe well beyond time-domain astronomy. The GTC equipped with OSIRIS+MAAT will also play a fundamental role in synergy with other facilities, some of them operating on the northern ORM at La Palma. This White Paper presents the different aspects of MAAT@GTC - including scientific and technical specifications, outstanding science cases, and an outline of the instrument concept., Comment: 49 pages, 36 figures

The purpose of this paper is to solve a kind of Riemann-Hilbert boundary value problem for $(\varphi,\psi)$-harmonic functions, which are linked with the use of two orthogonal basis of the Euclidean space $\mathbb{R}^m$. We approach this problem using the language of Clifford analysis for obtaining the explicit expression of the solution of the problem in a Jordan domain $\Omega\subset\mathbb{R}^m$ with fractal boundary. One of the remarkable feature in this study is that the boundary data involves higher order Lipschitz class of functions., Comment: 9 pages 0 figures

We prove that the Bredon cohomological dimension and the virtual cohomological dimension coincide for groups that admit a cocompact model for $\underline{E}G$ and satisfy properties (M) and (NM). Among the examples of groups satisfying these hypothesis are cocompact and arithmetic Fuchsian groups, one relator groups, the Hilbert modular group and $3$-manifold groups., Comment: Version accepted for publication in Glasgow Mathematical Journal. The title was changed, also some other minor corrections

We construct new examples of groups with cohomological dimension 2 and geometric dimension 3 with respect to the families of finite subgroups, virtually abelian groups of bounded rank, and the family of virtually poly-cyclic subgroups. Our main ingredients are the examples constructed by Brady-Leary-Nucinckis and Fluch-Leary, and Bass-Serre theory., Comment: Version accepted for publication in Proceedings of the AMS. Minor corrections

Let $G$ be a group and $\mathcal{F}$ be a family of subgroups closed under conjugation and subgroups. A model for the classifying space $E_{\mathcal{F}} G$ is a $G$-CW-complex $X$ such that every isotropy group belongs to $\mathcal{F}$, and for all $H\in \mathcal{F}$ the fixed point subspace $X^H$ is contractible. The group $G$ is of type $\mathcal{F}\text{-}\mathrm{F}_{n}$ if it admits a model for $E_\mathcal{F} G$ with $n$-skeleton with compact orbit space. The main result of the article provides is a characterization of $\mathcal{F}\text{-}\mathrm{F}_{n}$ analogue to Brown's criterion for $\mathrm{FP}_n$. As applications we provide criteria for this type of finiteness properties with respect to families to be preserved by finite extensions, a result that contrast with examples of Leary and Nucinkis. We also recover L\"uck's characterization of property $\underline{\mathrm{F}}_n$ in terms of the finiteness properties of the Weyl groups., Comment: Version accepted for publication in JPAA

The vast volume of data generated by modern astronomical surveys offers test beds for the application of machine-learning. It is important to evaluate potential existing tools and determine those that are optimal for extracting scientific knowledge from the available observations. We explore the possibility of using clustering algorithms to separate stellar populations with distinct chemical patterns. Star clusters are likely the most chemically homogeneous populations in the Galaxy, and therefore any practical approach to identifying distinct stellar populations should at least be able to separate clusters from each other. We applied eight clustering algorithms combined with four dimensionality reduction strategies to automatically distinguish stellar clusters using chemical abundances of 13 elements. Our sample includes 18 stellar clusters with a total of 453 stars. We use statistical tests showing that some pairs of clusters are indistinguishable from each other when chemical abundances from the Apache Point Galactic Evolution Experiment (APOGEE) are used. However, for most clusters we are able to automatically assign membership with metric scores similar to previous works. The confusion level of the automatically selected clusters is consistent with statistical tests that demonstrate the impossibility of perfectly distinguishing all the clusters from each other. These statistical tests and confusion levels establish a limit for the prospect of blindly identifying stars born in the same cluster based solely on chemical abundances. We find that some of the algorithms we explored are capable of blindly identify stellar populations with similar ages and chemical distributions in the APOGEE data. Because some stellar clusters are chemically indistinguishable, our study supports the notion of extending weak chemical tagging that involves families of clusters instead of individual clusters

Let G be the fundamental group of a connected, closed, orientable 3-manifold. We explicitly compute its virtually cyclic geometric dimension. Among the tools we use are the prime and JSJ decompositions of M, several push-out type constructions, as well as some Bredon cohomology computations.

The role of gas accretion in galaxy evolution is still a matter of debate. The presence of inflows of metal-poor gas that trigger star formation bursts of low metallicity has been proposed as an explanation for the local anti-correlation between star formation rate (SFR) and gas-phase metallicity ($\rm Z_g$) found in the literature. In the present study, we show how the anti-correlation is also present as part of a diversified range of behaviours for a sample of more than 700 nearby spiral galaxies from the SDSS IV MaNGA survey. We have characterized the local relation between SFR and $\rm Z_g$ after subtracting the azimuthally averaged radial profiles of both quantities. $60\%$ of the analyzed galaxies display a $\rm SFR-Z_g$ anti-correlation, with the remaining $40\%$ showing no correlation ($19\%$) or positive correlation ($21\%$). Applying a Random Forest machine-learning algorithm, we obtain that the slope of the correlation is mainly determined by the average gas-phase metallicity of the galaxy. Galaxy mass, $g-r$ colors, stellar age, and mass density seem to play a less significant role. This result is supported by the performed 2nd-order polynomial regression analysis. Thus, the local $\rm SFR-Z_g$ slope varies with the average metallicity, with the more metal-poor galaxies presenting the lowest slopes (i.e., the strongest $\rm SFR-Z_g$ anti-correlations), and reversing the relation for more metal-rich systems. Our results suggest that external gas accretion fuels star-formation in metal-poor galaxies, whereas in metal-rich systems the gas comes from previous star formation episodes., Comment: 22 pages, 11 figures. Accepted for publication in ApJ

We use data from 1222 late-type star-forming galaxies in the SDSS IV MaNGA survey to identify regions in which the gas-phase metallicity is anomalously-low compared to expectations from the tight empirical relation between metallicity and stellar surface mass-density at a given stellar mass. We find anomalously low metallicity (ALM) gas in 10% of the star-forming spaxels, and in 25% of the galaxies in the sample. The incidence rate of ALM gas increases strongly with both global and local measures of the specific star-formation rate, and is higher in lower mass galaxies and in the outer regions of galaxies. The incidence rate is also significantly higher in morphologically disturbed galaxies. We estimate that the lifetimes of the ALM regions are a few hundred Myr. We argue that the ALM gas has been delivered to its present location by a combination of interactions, mergers, and accretion from the halo, and that this infusion of gas stimulates star-formation. Given the estimated lifetime and duty cycle of such events, we estimate that the time-averaged accretion rate of ALM gas is similar to the star-formation rate in late type galaxies over the mass-range M$_* \sim10^9$ to 10$^{10}$ M$_{\odot}$., Comment: Accepted by ApJ

Correlations between the radio continuum, infrared and CO emission are known to exist for several types of galaxies and across several orders of magnitude. However, the low-mass, low-luminosity and low-metallicity regime of these correlations is not well known. A sample of metal-rich and metal-poor dwarf galaxies from the literature has been assembled to explore this extreme regime. The results demonstrate that the properties of dwarf galaxies are not simple extensions of those of more massive galaxies; the different correlations reflect different star-forming conditions and different coupling between the star formation and the various quantities. It is found that dwarfs show increasingly weaker CO and infrared emission for their luminosity, as expected for galaxies with a low dust content, slower reaction rates, and a hard ionizing radiation field. In the higher-luminosity dwarf regime (L_1.4GHz > 10^27 W, where L_1.4GHz ~ 10^29 W for a Milky Way star formation rate of ~1 M_sun yr^-1), the total and non-thermal radio continuum emission appear to adequately trace the star formation rate. A breakdown of the dependence of the (Halpha-based) thermal, non-thermal, and, hence, total radio continuum emission on star formation rate occurs below L_1.4GHz ~ 10^27 W, resulting in a steepening or downturn of the relations at extreme low luminosity. Below L_FIR ~ 10^36 W ~ 3 x 10^9 L_sun, the infrared emission ceases to adequately trace the star formation rate. A lack of a correlation between the magnetic field strength and the star formation rate in low star formation rate dwarfs suggests a breakdown of the equipartition assumption. As extremely metal-poor dwarfs mostly populate the low star formation rate and low luminosity regime, they stand out in their infrared, radio continuum and CO properties., Comment: accepted for publication in MNRAS

Let $G$ be a group, let $H$ be a subgroup of $G$ and let $\Or(G)$ be the orbit category. In this paper we extend the definition of the relative group (co)homology theories of the pair $(G,H)$ defined by Adamson and Takasu to have coefficients in an $\Or(G)$-module. There is a canonical comparison homomorphism defined by Cisneros-Molina and Arciniega-Nev\'arez from Takasu's theory to Adamson's one. We give a necessary and sufficient condition on the subgroup $H$ for which the comparison homomorphism is an isomorphism for all coefficients. We also use the L\"uck-Wiermann construction to introduce a long exact sequence for Adamson (co)homology. Finally, we provide some examples of explicit computations for the comparison homomorphism., Comment: Shortened version. This version was accepted for publication in Quaestiones Mathematicae

The claimed detection of a diffuse galaxy lacking dark matter represents a possible challenge to our understanding of the properties of these galaxies and galaxy formation in general. The galaxy, already identified in photographic plates taken in the summer of 1976 at the UK 48-in Schmidt telescope, presents normal distance-independent properties (e.g. colour, velocity dispersion of its globular clusters). However, distance-dependent quantities are at odds with those of other similar galaxies, namely the luminosity function and sizes of its globular clusters, mass-to-light ratio and dark matter content. Here we carry out a careful analysis of all extant data and show that they consistently indicate a much shorter distance (13 Mpc) than previously indicated (20 Mpc). With this revised distance, the galaxy appears to be a rather ordinary low surface brightness galaxy (R_e=1.4+-0.1 kpc; M*=6.0+-3.6x10^7 Msun) with plenty of room for dark matter (the fraction of dark matter inside the half mass radius is >75% and M_halo/M*>20) corresponding to a minimum halo mass >10^9 Msun. At 13 Mpc, the luminosity and structural properties of the globular clusters around the object are the same as those found in other galaxies., Comment: MNRAS, in press. This version includes an extra new independent distance indicator confirming the 13 Mpc distance. New tests also reject the possibility that blends are causing a misidentification of the location of the TRGB

A giant star-forming region in a metal-poor dwarf galaxy has been observed in optical lines with the 10-m Gran Telescopio Canarias and in the emission line of CO(1-0) with the NOEMA mm-wave interferometer. The metallicity was determined to be 12+log(O/H)=7.83+-0.09, from which we estimate a conversion factor of alpha_CO~100 Msun/pc2/(K km/s) and a molecular cloud mass of ~2.9x10^7 Msun. This is an enormous concentration of molecular mass at one end of a small galaxy, suggesting a recent accretion. The molecular cloud properties seem normal: the surface density, 120 Msun/pc2, is comparable to that of a standard giant molecular cloud, the cloud's virial ratio of ~1.8 is in the star-formation range, and the gas consumption time, 0.5 Gyr, at the present star formation rate is typical for molecular regions. The low metallicity implies that the cloud has an average visual extinction of only 0.8 mag, which is close to the threshold for molecule formation. With such an extinction threshold, molecular clouds in metal-poor regions should have high surface densities and high internal pressures. If high pressure is associated with the formation of massive clusters, then metal-poor galaxies such as dwarfs in the early universe could have been the hosts of metal-poor globular clusters., Comment: 4 pages and 4 figures. accepted by ApJL

The data volume generated by astronomical surveys is growing rapidly. Traditional analysis techniques in spectroscopy either demand intensive human interaction or are computationally expensive. In this scenario, machine learning, and unsupervised clustering algorithms in particular offer interesting alternatives. The Apache Point Observatory Galactic Evolution Experiment (APOGEE) offers a vast data set of near-infrared stellar spectra which is perfect for testing such alternatives. Apply an unsupervised classification scheme based on $K$-means to the massive APOGEE data set. Explore whether the data are amenable to classification into discrete classes. We apply the $K$-means algorithm to 153,847 high resolution spectra ($R\approx22,500$). We discuss the main virtues and weaknesses of the algorithm, as well as our choice of parameters. We show that a classification based on normalised spectra captures the variations in stellar atmospheric parameters, chemical abundances, and rotational velocity, among other factors. The algorithm is able to separate the bulge and halo populations, and distinguish dwarfs, sub-giants, RC and RGB stars. However, a discrete classification in flux space does not result in a neat organisation in the parameters space. Furthermore, the lack of obvious groups in flux space causes the results to be fairly sensitive to the initialisation, and disrupts the efficiency of commonly-used methods to select the optimal number of clusters. Our classification is publicly available, including extensive online material associated with the APOGEE Data Release 12 (DR12). Our description of the APOGEE database can enormously help with the identification of specific types of targets for various applications. We find a lack of obvious groups in flux space, and identify limitations of the $K$-means algorithm in dealing with this kind of data., Comment: 23 pages, 24 images and online material

The fourth generation of the Sloan Digital Sky Survey (SDSS-IV) has been in operation since July 2014. This paper describes the second data release from this phase, and the fourteenth from SDSS overall (making this, Data Release Fourteen or DR14). This release makes public data taken by SDSS-IV in its first two years of operation (July 2014-2016). Like all previous SDSS releases, DR14 is cumulative, including the most recent reductions and calibrations of all data taken by SDSS since the first phase began operations in 2000. New in DR14 is the first public release of data from the extended Baryon Oscillation Spectroscopic Survey (eBOSS); the first data from the second phase of the Apache Point Observatory (APO) Galactic Evolution Experiment (APOGEE-2), including stellar parameter estimates from an innovative data driven machine learning algorithm known as "The Cannon"; and almost twice as many data cubes from the Mapping Nearby Galaxies at APO (MaNGA) survey as were in the previous release (N = 2812 in total). This paper describes the location and format of the publicly available data from SDSS-IV surveys. We provide references to the important technical papers describing how these data have been taken (both targeting and observation details) and processed for scientific use. The SDSS website (www.sdss.org) has been updated for this release, and provides links to data downloads, as well as tutorials and examples of data use. SDSS-IV is planning to continue to collect astronomical data until 2020, and will be followed by SDSS-V., Comment: SDSS-IV collaboration alphabetical author data release paper. DR14 happened on 31st July 2017. 19 pages, 5 figures. Accepted by ApJS on 28th Nov 2017 (this is the "post-print" and "post-proofs" version; minor corrections only from v1, and most of errors found in proofs corrected)

In this paper we provide descriptions of the Whitehead groups with coefficients in a ring of the Hilbert modular group and its reduced version, as well as for the topological K-theory of $C^*$-algebras, after tensoring with $\mathbb{Q}$, by computing the source of the assembly maps in the Farrell-Jones and the Baum-Connes conjecture respectively. We also construct a model for the classifying space of the Hilbert modular group for the family of virtually cyclic subgroups.

We describe the structural, stellar population and gas properties of the nearest Ultra Diffuse Galaxy (UDG) discovered so far: UGC2162 (z=0.00392; R$_{e,g}$=1.7$(\pm$0.2) kpc; $\mu_g(0)$=24.4$\pm$0.1 mag/arcsec$^2$; g-i=0.33$\pm$0.02). This galaxy, located at a distance of 12.3($\pm$1.7) Mpc, is a member of the M77 group. UGC2162 has a stellar mass of $\sim$2($^{+2}_{-1}$)$\times$10$^7$ M$_\odot$ and is embedded within a cloud of HI gas $\sim$10 times more massive: $\sim$1.9($\pm$0.6)$\times$10$^8$ M$_\odot$. Using the width of its HI line as a dynamical proxy, the enclosed mass within the inner R$\sim$5 kpc is $\sim$4.6($\pm$0.8)$\times$10$^9$ M$_\odot$ (i.e. M/L$\sim$200). The estimated virial mass from the cumulative mass curve is $\sim$8($\pm$2)$\times$10$^{10}$ M$_\odot$. Ultra-deep imaging from the IAC Stripe82 Legacy Project show that the galaxy is irregular and has many star forming knots, with a gas-phase metallicity around one-third of the solar value. Its estimated Star Formation Rate (SFR) is $\sim$0.01 M$_\odot$/yr. This SFR would double the stellar mass of the object in $\sim$2 Gyr. If the object were to stop forming stars at this moment, after a passive evolution, its surface brightness would become extremely faint: $\mu_g(0)$$\sim$27 mag/arcsec$^2$ and its size would remain large R$_{e,g}$$\sim$ 1.8 kpc. Such faintness would make it almost undetectable to most present-day surveys. This suggests that there could be an important population of M$_{\star}$$\sim$10$^7$ M$_\odot$ "dark galaxies" in rich environments (depleted of HI gas) waiting to be discovered by current and future ultra-deep surveys., Comment: 5 pages; 3 figures, accepted for publication in ApJ; minor changes to match the published version

The tadpole galaxy Kiso 5639 has a slowly rotating disk with a drop in metallicity at its star-forming head, suggesting that star formation was triggered by the accretion of metal-poor gas. We present multi-wavelength HST WFC3 images of UV through I band plus Halpha to search for peripheral emission and determine the properties of various regions. The head has a mass in young stars of ~10^6 Mo and an ionization rate of 6.4x10^51 s^{-1}, equivalent to ~2100 O9-type stars. There are four older star-forming regions in the tail, and an underlying disk with a photometric age of ~1 Gyr. The mass distribution function of 61 star clusters is a power law with a slope of -1.73+-0.51. Fourteen young clusters in the head are more massive than 10^4 Mo, suggesting a clustering fraction of 30%-45%. Wispy filaments of Halpha emission and young stars extend away from the galaxy. Shells and holes in the head HII region could be from winds and supernovae. Gravity from the disk should limit the expansion of the HII region, although hot gas might escape through the holes. The star formation surface density determined from Halpha in the head is compared to that expected from likely pre-existing and accreted gas. Unless the surface density of the accreted gas is a factor of ~3 or more larger than what was in the galaxy before, the star formation rate has to exceed the usual Kennicutt-Schmidt rate by a factor of >5., Comment: 13 pages, 14 figures, 3 tables, accepted by ApJ

Massive high-redshift quiescent compact galaxies (nicknamed red nuggets) have been traditionally connected to present-day elliptical galaxies, often overlooking the relationships that they may have with other galaxy types. We use large bulge-disk decomposition catalogues based on the Sloan Digital Sky Survey (SDSS) to check the hypothesis that red nuggets have survived as compact cores embedded inside the haloes or disks of present-day massive galaxies. In this study, we designate a "compact core" as the bulge component that satisfies a prescribed compactness criterion. Photometric and dynamic mass-size and mass-density relations are used to show that, in the inner regions of galaxies at z ~ 0.1, there are "abundant" compact cores matching the peculiar properties of the red nuggets, an abundance comparable to that of red nuggets at z ~ 1.5. Furthermore, the morphology distribution of the present-day galaxies hosting compact cores is used to demonstrate that, in addition to the standard channel connecting red nuggets with elliptical galaxies, a comparable fraction of red nuggets might have ended up embedded in disks. This result generalises the inside-out formation scenario; present-day massive galaxies can begin as dense spheroidal cores (red nuggets), around which either a spheroidal halo or a disk are formed later., Comment: 17 pages, 14 figures. Revised to match published MNRAS version; minor editorial changes throughout and updated references, with no change to results. 2016MNRAS.457.1916D

Let $G$ be a word hyperbolic group. We prove that the algebraic $K$-theory groups of $\dbZ [G]$, $K_n(\dbZ[G])$, have finite rank for all $n\in \dbZ$. For a few classes of groups, we give explicit formulas for the ranks of the algebraic $K$-theory groups of their group rings., Comment: 9 pages, 1 figure

We prove the $K$ and $L$ theoretic versions of the Fibered Isomorphism Conjecture of F. T. Farrell and L. E. Jones for braid groups on a surface., Comment: To appear in OSU special year proceedings

We give formulas for the Whitehead groups and the rational $K$-theory groups of the (integer group ring of the) Hilbert modular group in terms of its maximal finite subgroups., Comment: 15 pages

Tadpole Galaxies look like a star forming head with a tail structure to the side. They are also named cometaries. In a series of recent works we have discovered a number of issues that lead us to consider them extremely interesting targets. First, from images, they are disks with a lopsided starburst. This result is firmly established with long slit spectroscopy in a nearby representative sample. They rotate with the head following the rotation pattern but displaced from the rotation center. Moreover, in a search for extremely metal poor (XMP) galaxies, we identified tadpoles as the dominant shapes in the sample- nearly 80% of the local XMP galaxies have a tadpole morphology. In addition, the spatially resolved analysis of the metallicity shows the remarkable result that there is a metallicity drop right at the position of the head. This is contrary to what intuition would say and difficult to explain if star formation has happened from gas processed in the disk. The result could however be understood if the star formation is driven by pristine gas falling into the galaxy disk. If confirmed, we could be unveiling, for the first time, cool flows in action in our nearby world. The tadpole class is relatively frequent at high redshift - 10% of resolvable galaxies in the Hubble UDF but less than 1% in the local Universe. They are systems that could track cool flows and test models of galaxy formation., Comment: arXiv admin note: text overlap with arXiv:1302.4352

Local UV-bright galaxies in the Kiso survey include clumpy systems with kpc-size star complexes that resemble clumpy young galaxies in surveys at high redshift. We compare clump masses and underlying disks in several dozen galaxies from each of these surveys to the star complexes and disks of normal spirals. Photometry and spectroscopy for the Kiso and spiral sample come from the Sloan Digital Sky Survey. We find that the largest Kiso clumpy galaxies resemble UDF clumpies in terms of the star formation rates, clump masses, and clump surface densities. Clump masses and surface densities in normal spirals are smaller. If the clump masses are proportional to the turbulent Jeans mass in the interstellar medium, then for the most luminous galaxies in the sequence of normal:Kiso:UDF, the turbulent speeds and surface densities increase in the proportions 1.0:4.7:5.0 and 1.0:4.0:5.1, respectively, for fixed restframe B-band absolute magnitude. For the least luminous galaxies in the overlapping magnitude range, the turbulent speed and surface density trends are 1.0:2.7:7.4 and 1.0:1.4:3.0, respectively. We also find that while all three types have radially decreasing disk intensities when measured with ellipse-fit azimuthal averages, the average profiles are more irregular for UDF clumpies (which are viewed in their restframe UV) than for Kiso galaxies (viewed at g-band), and major axis intensity scans are even more irregular for the UDF than Kiso galaxies. Local clumpy galaxies in the Kiso survey appear to be intermediate between UDF clumpies and normal spirals., Comment: 24 pages, 15 figures, ApJ, in press