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Inter-modulo arithmetic operations, such as reverse conversion and scaling, are important but difficult operations in the RNS domain. This paper proposes efficient arithmetic units to perform this hard class of RNS operations for a new family of augmented three-moduli sets { 2 n + k, 2 n − 1, 2 n + 1 − 1 } (0 ≤ k ≤ n) ⁠. Experimental results for 65 nm CMOS technology show that the proposed reverse converter reduces the delay by about (17.6 − 33.4) % in comparison with the state of the art. Moreover, this work presents the first architecture of a scaler dedicated for this augmented three-moduli sets. [ABSTRACT FROM AUTHOR]

This paper provides a general operadic definition for the notion of splitting the operations of algebraic structures. This construction is proved to be equivalent to some Manin products of operads in the case of quadratic operads and it is shown to be closely related to Rota–Baxter operators. Hence, it gives a new effective way to compute Manin black products. Finally, this allows us to describe the algebraic structure of square matrices with coefficients in algebras of certain types. Many examples illustrate this text, including an example of nonquadratic algebras with Jordan algebras. [ABSTRACT FROM PUBLISHER]

Let be a finite Chevalley group defined over the field of q=pr elements, and k be an algebraically closed field of characteristic p>0. A fundamental open and elusive problem has been the computation of the cohomology ring . In this paper, we determine initial vanishing ranges, which improves upon known results. For root systems of type An and Cn, the first nontrivial cohomology classes are determined when p is larger than the Coxeter number (larger than twice the Coxeter number for type An with n>1 and r>1). In the process we make use of techniques involving line bundle cohomology for the flag variety G/B and its relation to combinatorial data from Kostant Partition Functions. [ABSTRACT FROM PUBLISHER]

Integral cluster categories of acyclic quivers have recently been used in the representation-theoretic approach to quantum cluster algebras. We show that over a principal ideal domain, such categories behave much better than one would expect: They can be described as orbit categories, their indecomposable rigid objects do not depend on the ground ring and the mutation operation is transitive. [ABSTRACT FROM PUBLISHER]

The purpose of this article is to construct a Hecke equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Hilbert–Blumenthal varieties with nonconstant algebraic coefficients. [ABSTRACT FROM PUBLISHER]

We investigate the implications of Gromov’s theorem on boundedness of primary characteristic classes for the continuous bounded cohomology of a semisimple Lie group G. We deduce that the comparison map from continuous bounded cohomology to continuous cohomology is surjective for a large class of semisimple Lie groups, including all Hermitian groups. Our proof is based on a geometric implementation of the canonical map from the cohomology of the classifying space of G to the continuous group cohomology of G. We obtain this implementation by establishing a variant of Kobayashi–Ono–Hirzebruch duality. [ABSTRACT FROM PUBLISHER]

We study Hochschild (co)homology groups of the Dunkl operator quantization of -singularity constructed by Halbout and Tang. Further, we study traces on this algebra and prove a local algebraic index formula. [ABSTRACT FROM PUBLISHER]

In this paper, we prove the dg affinity of formal deformation algebroid stacks over complex smooth algebraic varieties. For that purpose, we introduce the triangulated category of formal deformation modules which are cohomologically complete and whose associated graded module is quasi-coherent. [ABSTRACT FROM PUBLISHER]

Infinite-dimensional Hamiltonian systems appear naturally in the rich algebraic structure of symplectic field theory. Carefully defining a generalization of gravitational descendants and adding them to the picture, one can produce an infinite number of symmetries of such systems. As in Gromov–Witten theory, the study of the topological meaning of gravitational descendants yields new differential equations for the SFT Hamiltonian, where the key point is to understand the dependence of the algebraic constructions on choices of auxiliary data such as differential forms representing cohomology classes on the target and coherent collections of sections used to define gravitational descendants. [ABSTRACT FROM PUBLISHER]

An origami manifold is a manifold equipped with a closed 2-form which is symplectic except on a hypersurface, where it is like the pullback of a symplectic form by a folding map and its kernel fibrates with oriented circle fibers over a compact base. We can move back and forth between origami and symplectic manifolds using cutting (unfolding) and radial blow-up (folding), modulo compatibility conditions. We prove an origami convexity theorem for Hamiltonian torus actions, classify toric origami manifolds by polyhedral objects resembling paper origami and discuss examples. We also prove a cobordism result and compute the cohomology of a special class of origami manifolds. [ABSTRACT FROM PUBLISHER]

We observe that the Poincaré duality isomorphism for a string manifold is an isomorphism of modules over the subalgebra of the modulo 2 Steenrod algebra. In particular, the pattern of the operations Sq1, Sq2, and Sq4 on the cohomology of a string manifold has a symmetry around the middle dimension. We characterize this kind of cohomology operation duality in terms of the annihilator of the Thom class of the negative tangent bundle, and in terms of the vanishing of top-degree cohomology operations. We also indicate how the existence of such an operation-preserving duality implies the integrality of certain polynomials in the Pontryagin classes of the manifold. [ABSTRACT FROM PUBLISHER]

A simple characterization of topological amenability in terms of bounded cohomology is proved, following Johnson’s formulation of amenability. The connection to injective Banach modules is established. [ABSTRACT FROM PUBLISHER]

We describe an application of Poincaré duality for completed homology spaces (as defined by Emerton) to level raising for p-adic modular forms. This allows us to give a new description of the image of Chenevier’s p-adic Jacquet–Langlands map between an eigencurve for a definite quaternion algebra and an eigencurve for GL2. The points on the eigencurve at which we “raise the level” are (nonsmooth) points of intersection between an “old” and a “new” component. [ABSTRACT FROM PUBLISHER]

The cohomology of an arithmetically defined subgroup of the symplectic ℚ-group Spn is closely related to the theory of automorphic forms. This paper gives a structural account of that part of the cohomology, which is generated by residues or derivatives of Eisenstein series of relative rank one. In particular, we determine a set of conditions subject to which residues of Eisenstein series may give rise to non-vanishing cohomology classes. A non-vanishing condition on the value at s = 1/2 of certain automorphic L-functions, which naturally appear in the constant terms of the Eisenstein series, plays a major role. [ABSTRACT FROM PUBLISHER]

We study the topology of the moduli space of flat SU(2)-bundles over a non-orientable surface Σ. This moduli space may be identified with the space of homomorphisms Hom (π1(Σ), SU(2)) modulo conjugation by SU(2). In particular, we compute the (rational) equivariant cohomology ring of Hom (π1(Σ), SU(2)) and use this to compute the ordinary cohomology groups of the quotient Hom (π1(Σ), SU(2))/SU(2). A key property is that the conjugation action is equivariantly formal. [ABSTRACT FROM PUBLISHER]

We show how to compute a certain group of equivalence classes of invariant Drinfeld twists on the algebra of a finite group G over a field k of characteristic zero. This group is naturally isomorphic to the second lazy cohomology group of the Hopf algebra of k-valued functions on G. When k is algebraically closed, the answer involves the group of outer automorphisms of G induced by conjugation in the group algebra as well as the set of all pairs (A, b), where A is an abelian normal subgroup of G and is a k×-valued G-invariant nondegenerate alternating bilinear form on the dual . When the ground field k is not algebraically closed, we use algebraic group techniques to reduce the computation of Hℓ2(G) to a computation over the algebraic closure. As an application of our results, we compute Hℓ2(G) for a number of groups. [ABSTRACT FROM PUBLISHER]

In this paper, we provide a wildness criterion for any finite dimensional Hopf algebra with finitely generated cohomology. This generalizes a result of Farnsteiner to not necessarily cocommutative Hopf algebras over ground fields of arbitrary characteristic. Our proof uses the theory of support varieties for modules, one of the crucial ingredients being a tensor product property for some special modules. As an application, we prove a conjecture of Cibils stating that small quantum groups of rank at least two are wild. [ABSTRACT FROM PUBLISHER]

Building on the recent determination of the simplicial cohomology groups of the convolution algebra ℓ1(ℤk+) [F. Gourdeau, Z. A. Lykova and M. C. White, A Künneth formula in topological homology and its applications to the simplicial cohomology of ℓ1(ℤk+), Studia Math. 166 (2005), 29–54], we investigate what can be said for the cohomology of this algebra with more general symmetric coefficients. Our approach leads us to a discussion of the Harrison homology and cohomology in the context of Banach algebras and a development of some of its basic features. As an application of our techniques, we reprove some known results on second-degree cohomology. [ABSTRACT FROM PUBLISHER]

The subset complex Δ(G) of a finite group G is defined as the simplicial complex whose simplices are non-empty subsets of G. The oriented chain complex of Δ(G) gives a ℤG-module extension of ℤ by ℤ̃, where ℤ̃ is a copy of integers on which G acts via the sign representation of the regular representation. The extension class ζG ∈ ExtℤG|G|−1 (ℤ, ℤ̃) of this extension is called the Ext class or the Euler class of the subset complex Δ (G). This class was first introduced by Reiner and Webb [The combinatorics of the bar resolution in group cohomology, J. Pure Appl. Algebra 190 (2004), 291–327] who also raised the following question: What are the finite groups for which ζG is non-zero? [ABSTRACT FROM PUBLISHER]

Locally conformally Kähler (LCK) manifolds with potential are those which admit a Kähler covering with a proper, automorphic, global potential. The existence of a potential can be characterized cohomologically as vanishing of a certain cohomology class, called the Bott–Chern class. Compact LCK manifolds with potential are stable at small deformations and admit holomorphic embeddings into Hopf manifolds. This class strictly includes the Vaisman manifolds. We show that every compact LCK manifold with potential can be deformed into a Vaisman manifold. Therefore, every such manifold is diffeomorphic to a smooth elliptic fibration over a Kähler orbifold. We show that the pluricanonical condition on LCK manifolds introduced by G. Kokarev is equivalent to vanishing of the Bott–Chern class. This gives a simple proof of some of the results on topology of pluricanonical LCK manifolds, discovered by Kokarev and Kotschick. [ABSTRACT FROM PUBLISHER]

Étale Nori finite vector bundles are the bundles defined by representations of a finite étale group scheme in the usual way. In this article, we show that in many cases the dimensions of the Hodge cohomology groups of such a vector bundle and a twist of it by an automorphism of the ground field are the same. This generalizes to the higher rank case the result of Pink–Roessler [13, Proposition 3.5]. [ABSTRACT FROM PUBLISHER]

We show that in closed string topology and in open-closed string topology with one D-brane, higher genus stable string operations are trivial. This is a consequence of Harer's stability theorem and related stability results on the homology of mapping class groups of surfaces with boundaries. In fact, this vanishing result is a special case of a general result that applies to all homological conformal field theories with the property that in the associated topological quantum field theories, the string operations associated to genus 1 cobordisms with one or two boundaries vanish. In closed string topology, the base manifold can be either finite-dimensional, or infinite-dimensional with finite-dimensional cohomology for its based loop space. The above vanishing result is based on the triviality of string operations associated to the homology classes of mapping class groups that are in the image of stabilizing maps. [ABSTRACT FROM PUBLISHER]

Equivariant Hirzebruch genera of a variety X acted upon by a finite group of algebraic automorphisms are defined by combining the group action with the information encoded by the Hodge filtration in cohomology. For smooth manifolds, Atiyah and Meyer studied contributions of monodromy to usual signatures. While for a projective manifold equivariant genera can by computed by the Atiyah–Singer holomorphic Lefschetz theorem, we derive a Atiyah–Meyer-type formula for such genera even when X is not necessarily smooth or compact, but just fibers equivariantly (in the complex topology) over an algebraic manifold. These results apply to computing Hirzebruch invariants of orbit spaces. We also obtain results comparing equivariant genera of the range and domain of an equivariant morphism in terms of its singularities. [ABSTRACT FROM PUBLISHER]

In this paper, we show that homotopy K3 surfaces do not admit a periodic diffeomorphism of odd prime order 3 acting trivially on cohomology. This gives a negative answer for period 3 to Problem 4.124 in Kirby's problem list. In addition, we give an obstruction in terms of the rationality and the sign of the spin numbers to the non-existence of a periodic diffeomorphism of odd prime order acting trivially on cohomology of homotopy K3 surfaces. The main strategy is to calculate the Seiberg–Witten invariant for the trivial spinc structure in the presence of such a Zp-symmetry in two ways: (1) the new interpretation of the Seiberg–Witten invariants of Furuta and Fang, and (2) the theorem of Morgan and Szabó on the Seiberg–Witten invariant of homotopy K3 surfaces for the trivial Spinc structure. As a consequence, we derive a contradiction for any periodic diffeomorphism of prime order 3 acting trivially on cohomology of homotopy K3 surfaces. [ABSTRACT FROM PUBLISHER]

We prove the existence of a Čech cohomology theory in arbitrary o-minimal structures with definable Skolem functions satisfying the Eilenberg–Steenrod axioms. [ABSTRACT FROM PUBLISHER]

In this paper, we discuss the application of hierarchical matrix techniques to the solution of Helmholtz problems with large wave number κ in 2D. We consider the Brakhage–Werner integral formulation of the problem discretized by the Galerkin boundary-element method. The dense n × n Galerkin matrix arising from this approach is represented by a sum of an -matrix and an 2-matrix, two different hierarchical matrix formats. A well-known multipole expansion is used to construct the 2-matrix. We present a new approach to dealing with the numerical instability problems of this expansion: the parts of the matrix that can cause problems are approximated in a stable way by an -matrix. Algebraic recompression methods are used to reduce the storage and the complexity of arithmetical operations of the -matrix. Further, an approximate LU decomposition of such a recompressed -matrix is an effective preconditioner. We prove that the construction of the matrices as well as the matrix-vector product can be performed in almost linear time in the number of unknowns. Numerical experiments for scattering problems in 2D are presented, where the linear systems are solved by a preconditioned iterative method. [ABSTRACT FROM PUBLISHER]

The purpose of this paper is to study and compare the collapsing of two spectral sequences converging to the cohomology of a configuration space. The noncollapsing of these spectral sequences is related, in some cases, to the existence of Massey products in the cohomology of the manifold M. [ABSTRACT FROM AUTHOR]

The article discusses the connections between the existence of projection with a w*-closed kernel in the w*-closure of an approximating sequence and the creation of commuting approximating sequences. It explores how any separable Banach space with (UMAP) possess an approximating sequence that satisfies two operations. It also tackles the construction of commuting approximating sequences and the unconditional metric approximation property.

We study the rational cohomology groups of the real De Concini–Procesi model corresponding to a finite Coxeter group, generalizing the type-A case of the moduli space of stable genus 0 curves with marked points. We compute the Betti numbers in the exceptional types, and give formulae for them in types B and D. We give a generating-function formula for the characters of the representations of a Coxeter group of type B on the rational cohomology groups of the corresponding real De Concini–Procesi model, and deduce the multiplicities of one-dimensional characters in the representations, and a formula for the Euler character. We also give a moduli space interpretation of this type-B variety, and hence show that the action of the Coxeter group extends to a slightly larger group. [ABSTRACT FROM PUBLISHER]

We show that H-spaces with finitely generated cohomology, as an algebra or as an algebra over the Steenrod algebra, have homotopy exponents at all primes. This provides a positive answer to a question of Stanley. [ABSTRACT FROM PUBLISHER]

Let X be a compact connected Riemann surface of genus at least two. We compute the Chen–Ruan cohomology ring of the moduli space of stable –bundles over X of the nontrivial second Stiefel–Whitney class. [ABSTRACT FROM PUBLISHER]

We study families of complex Monge–Ampère equations, focusing on the case where the cohomology classes degenerate to a nonbig class. We establish uniform a priori L∞-estimates for the normalized solutions, generalizing the recent work of S. Kołodziej and G. Tian. This has interesting consequences in the study of the Kähler–Ricci flow. [ABSTRACT FROM PUBLISHER]

Let E be an elliptic curve defined over and let be a finite Galois extension with Galois group G. The equivariant Birch–Swinnerton–Dyer conjecture for viewed as a motive over with coefficients in relates the twisted L-values associated with E with the arithmetic invariants of the same. In this paper I prescribe an approach to verify this conjecture for a given data. Using this approach, we verify the conjecture for an elliptic curve of conductor 11 and an S3-extension of . [ABSTRACT FROM PUBLISHER]

We study holomorphic Poisson manifolds and holomorphic Lie algebroids from the viewpoint of real Poisson geometry. We give a characterization of holomorphic Poisson structures in terms of the Poisson Nijenhuis structures of Magri–Morosi and describe a double complex that computes the holomorphic Poisson cohomology. A holomorphic Lie algebroid structure on a vector bundle A → X is shown to be equivalent to a matched pair of complex Lie algebroids (T0,1 X, A1,0), in the sense of Lu. The holomorphic Lie algebroid cohomology of A is isomorphic to the cohomology of the elliptic Lie algebroid T0,1 X ⋈ A1,0. In the case when (X,π) is a holomorphic Poisson manifold and A = (T*X)π, such an elliptic Lie algebroid coincides with the Dirac structure corresponding to the associated generalized complex structure of the holomorphic Poisson manifold. [ABSTRACT FROM PUBLISHER]

We explore the codimension-one strata in the degree-one cohomology jumping loci of a finitely generated group, through the prism of the multivariable Alexander polynomial. As an application, we give new criteria that must be satisfied by fundamental groups of smooth, quasi-projective complex varieties. These criteria establish precisely which fundamental groups of boundary manifolds of complex line arrangements are quasi-projective. We also give sharp upper bounds for the twisted Betti ranks of a group, in terms of multiplicities constructed from the Alexander polynomial. For Seifert links in homology 3-spheres, these bounds become equalities, and our formula shows explicitly how the Alexander polynomial determines all the characteristic varieties. [ABSTRACT FROM PUBLISHER]

The Hard Lefschetz Theorem (HLT) and the Hodge–Riemann bilinear relations (HRR) hold in various contexts: they impose restrictions on the cohomology algebra of a smooth compact Kähler manifold; they restrict the local monodromy of a polarized variation of Hodge structure; they impose conditions on the f-vectors of convex polytopes. While the statements of these theorems depend on the choice of a Kähler class, or its analog, there is usually a cone of possible choices. It is then natural to ask whether the HLT and HRR remain true in a mixed context. In this note, we present a unified approach to proving the mixed HLT and HRR, generalizing the known results, and proving it in new cases, such as the intersection cohomology of nonrational polytopes. [ABSTRACT FROM PUBLISHER]

Boe, Kujawa and Nakano [3; 4] recently investigated relative cohomology for classical Lie superalgebras and developed a theory of support varieties. The dimensions of these support varieties give a geometric interpretation of the combinatorial notions of defect and atypicality due to Kac, Wakimoto, and Serganova. In this paper, we calculate the cohomology ring of the Cartan-type Lie superalgebra W(n) relative to the degree zero component W(n)0 and show that this ring is a finitely generated polynomial ring. This allows one to define support varieties for finite-dimensional W(n)-supermodules, which are completely reducible over W(n)0. We calculate the support varieties of all simple supermodules in this category. The outcome of our computations naturally divides the simple supermodules into two families. Remarkably, this partition coincides with the one based on Serganova's prior notion of atypicality for Cartan-type superalgebras. In this way the support variety construction gives a geometric interpretation of atypicality. We also present new results on the realizability of support varieties, which hold for both classical and Cartan-type superalgebras. [ABSTRACT FROM PUBLISHER]

We use the Brill–Noether theory to prove the Green conjecture for exceptional curves on K3 surfaces. Such curves count among the few ones having Clifford dimension 3. We obtain our result by adopting an infinitesimal approach due to Pareschi, and using the degenerate version of the Hirschowitz–Ramanan–Voisin theorem obtained in the paper [4]. [ABSTRACT FROM PUBLISHER]

Investigates the relationship between multiplicative unstable cohomology operations and commutative graded formal group laws for certain important class of theories. Maps of homotopy ring spaces; Detection of categories and operations; Related theorems and their proofs; Application to additive multiplicative idempotents.