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We introduce the adjoint homological Selmer module for an $\textrm {SL}_2$-representation of a knot group, which may be seen as a knot theoretic analogue of the dual adjoint Selmer module for a Galois representation. We then show finitely generated torsion-ness of our adjoint Selmer module, which are widely known as conjectures in number theory, and give some concrete examples.

Lactobacillus delbrueckii subsp. delbrueckii TUA4408L is able to differentially modulate the innate immune response of porcine intestinal epithelial cells triggered by TLR4 activation. This strain also has a remarkable ability to grow on plant substrates. These two immunological and biotechnological characteristics prompted us to evaluate whether the soymilk by-product okara fermented with the TUA4408L strain can serve as an immunobiotic feed with the ability to beneficially modulate the intestinal immunity of piglets after weaning to improve their productivity. Our in vivo studies demonstrated that the administration of immunobiotic TUA4408L-fermented okara feed significantly increased piglet growth performance and meat quality. These positive effects were associated with the ability of the TUA4408L-fermented okara feed to beneficially modulate both intestinal microbiota and immunity in pigs. The immunobiotic feed improved the abundance of the beneficial bacteria Lactobacillus and Lactococcus in the gut of pigs, reduced blood markers of inflammation, and differentially regulated the expression of inflammatory and regulatory cytokines in the intestinal mucosa. These findings indicate that the immunobiotic TUA4408L-fermented okara feed could be an economical and environmentally friendly option to improve the growth performance and immune health of pigs. Fil: Suda, Yoshihito. Miyagi University; Japón Fil: Sasaki, Nana. Miyagi University; Japón Fil: Kagawa, Kyoma. Miyagi University; Japón Fil: Elean, Mariano Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Centro de Referencia para Lactobacilos; Argentina Fil: Zhou, Binghui. Tohoku University; Japón Fil: Tomokiyo, Mikado. Tohoku University; Japón Fil: Islam, Md Aminul. Tohoku University; Japón. Bangladesh Agricultural University; Bangladesh Fil: Shahid Riaz Rajoka, Muhammad. Tohoku University; Japón Fil: Humayun Kober, A.K.M.. Tohoku University; Japón. Chittagong Veterinary and Animal Sciences University; Bangladesh Fil: Shimazu, Tomoyuki. Miyagi University; Japón Fil: Egusa, Shintaro. No especifíca; Fil: Terashima, Yuji. No especifíca; Fil: Aso, Hisashi. Tohoku University; Japón Fil: Ikeda Ohtsubo, Wakako. Tohoku University; Japón Fil: Villena, Julio Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Centro de Referencia para Lactobacilos; Argentina Fil: Kitazawa, Haruki. Tohoku University; Japón

Streptococcal toxic shock syndrome (STSS) caused by Streptococcus pyogenes emm 89 strains has been increasing in several countries and reported to be linked with a recently emerged clade of emm89 strains, designated clade 3. In Japan, epidemiological and genetic information for emm89 strains remains elusive. In this study, we utilized emm89 strains isolated from both STSS (89 isolates) and non-STSS (72 isolates) infections in Japan from 2011 to 2019, and conducted whole-genome sequencing and comparative analysis, which resulted in classification of a large majority into clade 3 regardless of disease severity. In addition, STSS-associated genes and SNPs were found in clade 3 strains, including mutations of streptokinase (Ska), control of virulence sensor (CovS), serum opacity factor (SOF), sortase (SrtB), and fibronectin-binding protein F1 (PrtF1), and absence of the hylP1 gene encoding hyaluronidase. These findings provide insights into notable genetic features of emm89 strains.

We study the twisted knot module for the universal deformation of an SL 2 \textrm {SL}_2 -representation of a knot group and introduce an associated L L -function, which may be seen as an analogue of the algebraic p p -adic L L -function associated to the Selmer module for the universal deformation of a Galois representation. We then investigate two problems proposed by Mazur: Firstly we show the torsion property of the twisted knot module over the universal deformation ring under certain conditions. Secondly we compute the L L -function by some concrete examples for 2 2 -bridge knots.

We advocate the use of cluster algebras and their y-variables in the study of hyperbolic 3-manifolds. We study hyperbolic structures on the mapping tori of pseudo-Anosov mapping classes of punctured surfaces, and show that cluster y-variables naturally give the solutions of the edge-gluing conditions of ideal tetrahedra. We also comment on the completeness of hyperbolic structures., v2: 26 pages, 17 figures

In this paper, for a Seifert loop (i.e., a knot in a Seifert three-manifold), first we give a family of an explicit function $\Phi(q; N)$ whose special values at roots of unity are identified with the Witten-Reshetikhin-Turaev invariants of the Seifert loop for the integral homology sphere. Second, we show that the function $\Phi(q; N)$ satisfies a $q$-difference equation whose classical limit coincides with a component of the character varieties of the Seifert loop. Third, we give an interpretation of the function $\Phi(q; N)$ from the view point of the resurgent analysis., Comment: 23 pages, 1 figure. References are added in v3

In this paper, we show that Alexander polynomials for any 2-bridge knots are specializations of cluster variables. A key tool is an ancestral triangle which appeared in both quantum topology and hyperbolic geometry in different ways., 33 pages: typos corrected, detailed examples added in section 4

Based on the analogies between knot theory and number theory, we study a deformation theory for SL_2-representations of knot groups, following after Mazur's deformation theory of Galois representations. Firstly, by employing the pseudo-SL_2-representations, we prove the existence of the universal deformation of a given SL_2-representation of a finitely generated group Pi over a field whose characteristic is not 2. We then show its connection with the character scheme for SL_2-representations of Pi when k is an algebraically closed field. We investigate examples concerning Riley representations of 2-bridge knot groups and give explicit forms of the universal deformations. Finally we discuss the universal deformation of the holonomy representation of a hyperbolic knot group in connection with Thurston's theory on deformations of hyperbolic structures., Comment: 25 pages, to appear in Tohoku Math. J; corrected typos

A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop, we introduce a quantity called a partition q-series. The partition q-series are invariant under pentagon moves. If the quivers are of Dynkin type or square products thereof, they reproduce so-called parafermionic or quasi-particle character formulas of certain modules associated with affine Lie algebras. They enjoy nice modular properties as expected from the conformal field theory point of view., 20 pages, amslatex; typos corrected; published version

We give a finite-dimensional and geometric construction of a Chern character for twisted K-theory, introducing a notion of connection on a twisted vectorial bundle which can be considered as a finite-dimensional approximation of a twisted family of Fredholm operators. Our construction is applicable to the case of any classes giving the twisting, and agrees with the Chern character of bundle gerbe modules in the case of torsion classes.

In this paper, we show that discrete torsion phases in string orbifold partition functions, and membrane discrete torsion phases, are topological actions on the simplicial manifolds associated to orbifold group actions. For this purpose, we introduce an integration theory of smooth Deligne cohomology on a general simplicial manifold, and prove that the integration induces a well-defined paring between the smooth Deligne cohomology and the singular cycles.

We introduce a multiple generalization of the tame symbol, called {\em polysymbols}, associated to meromorphic functions on a Riemann surface as the Massey products in Deligne cohomology, and also give a geometric construction of polysymbols using Chen's iterated integrals. We then deduce some basic properties of polysymbols using our holonomy formula, and show that trivializations of polysymbols give variations of mixed Hodge structure.

In this paper, defining Poisson functions on super manifolds, we show that the graphs of Poisson functions are Dirac structures, and find Poisson functions which include as special cases both quasi-Poisson structures and twisted Poisson structures.

In this paper, first we introduce a quantity called a partition function for a quiver mutation sequence. The partition function is a generating function whose weight is a $q$-binomial associated with each mutation. Then, we show that the partition function can be expressed as a ratio of products of quantum dilogarithms. This provides a systematic way of constructing various $q$-binomial multisum identities., Comment: 19 pages

Ihara initiated to study a certain Galois representation which may be seen as an arithmetic analogue of the Artin representation of a pure braid group. We pursue the analogies in Ihara theory further, following after some issues and their inter-relations in the theory of braids and links such as Milnor invariants, Johnson homomorphisms, Magnus-Gassner cocycles and Alexander invariants, and study relations with arithmetic in Ihara theory., Comment: 66pages, to appear in Publ. Res. Inst. Math. Sci., corrected typos

In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algberas of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham complex on the base space, and show that the induced map on cohomology groups is independent of the choices. Moreover, we show that applying the construction to a surface bundle, our construction gives Morita-Mumford-Miller classes., Comment: 16 pages, 1 figure

In our previous work [arXiv:1403.6569], we introduced the partition q-series for mutation loop --- a loop in exchange quiver. In this paper, we show that for certain class of mutation sequences, called reverse-ending mutation loops, a graded version of partition q-series essentially coincides with the ordered product of quantum dilogarithm associated with each mutation; the partition q-series provides a state-sum description of combinatorial Donaldson-Thomas invariants introduced by B. Keller., 24 pages, published version

We propose a new description of 3d theories which do not admit conventional Lagrangians. Given a quiver and a mutation sequence on it, we define a 3d theory in such a way that the partition function of the theory coincides with the cluster partition function defined from the pair . Our formalism includes the case where 3d theories arise from the compactification of the 6d theory on a large class of 3-manifolds , including complements of arbitrary links in . In this case the quiver is defined from a 2d ideal triangulation, the mutation sequence represents an element of the mapping class group, and the 3-manifold is equipped with a canonical ideal triangulation. Our partition function then coincides with that of the holomorphic part of the ChernSimons partition function on .

We provide quantitative evidence for our previous conjecture which states an equivalence of the partition function of a 3d $\mathcal{N}=2$ gauge theory on a duality wall and that of the $SL(2,\mathbb{R})$ Chern-Simons theory on a mapping torus, for a class of examples associated with once-punctured torus. In particular, we demonstrate that a limit of the 3d $\mathcal{N}=2$ partition function reproduces the hyperbolic volume and the Chern-Simons invariant of the mapping torus. This is shown by analyzing the classical limit of the trace of an element of the mapping class group in the Hilbert space of the quantum Teichm\"uller theory. We also show that the subleading correction to the partition function reproduces the Reidemeister torsion.

We introduce non-acyclic $PGL_n(\mathbb{C})$-torsion of a 3-manifold with toroidal boundary as an extension of J. Porti's $PGL_2(\mathbb{C})$-torsion, and present an explicit formula of the $PGL_n(\mathbb{C})$-torsion of a mapping torus for a surface with punctures, by using the higher Teichm\"{u}ler theory due to V. Fock and A. Goncharov. Our formula gives a concrete rational function which represents the torsion function and comes from a concrete cluster transformation associated with the mapping class., Comment: 17 pages, 2 figures; 19 pages, 2 figures, to appear in Geometriae Dedicata

We propose an approach to study non-Abelian Iwasawa theory, using the idea of Johnson homomorphisms in low dimensional topology. We introduce arithmetic analogues of Johnson homomorphisms/maps, called the p-Johnson homomorphisms/maps, associated to the Zassenhaus filtration of a pro-p Galois group over a Z_p-extension of a number field. We give their cohomological interpretation in terms of Massey products in Galois cohomology., Comment: 38 pages, to appear in J. of Algebra, changed title from "p-Johnson homomorphisms in non-Abelian Iwasawa theory", added references in section 5, corrected typos

We show that the smooth geometry of a hyperbolic 3-manifold emerges from a classical spin system defined on a 2D discrete lattice, and moreover, show that the process of this ``dimensional oxidation'' is equivalent with the dimensional reduction of a supersymmetric gauge theory from 4D to 3D. More concretely, we propose an equality between (1) the 4D superconformal index of a 4D $\mathcal{N}=1$ superconformal quiver gauge theory described by a bipartite graph on ${T}^{2}$ and (2) the partition function of a classical integrable spin chain on ${T}^{2}$. The 2D spin system is lifted to a hyperbolic 3-manifold after the dimensional reduction and using the Higgs mechanism in the 4D gauge theory.

We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d N=2 superconformal field theory on S^3, which is realized as a duality domain wall in a 4d gauge theory on S^4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmuller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.