Related papers: The cyclic bar construction and fundamental groups
We prove the graded braided commutativity of the Hochschild cohomology of $A$ with trivial coefficients, where $A$ is a braided Hopf algebra in the category of Yetter-Drinfeld modules over the group algebra of an abelian group, under some…
The algebra of truncated polynomials A_m=Z[x]/(x^m) plays an important role in the theory of Khovanov and Khovanov-Rozansky homology of links. We have demonstrated that Hochschild homology is closely related to Khovanov homology via…
We compute the Hochschild cohomology groups $\HH^*(A)$ in case $A$ is a triangular string algebra, and show that its ring structure is trivial.
In this paper, we evaluate the algebraic $K$-groups of a planar cuspidal curve over a perfect $\mathbb{F}_p$-algebra relative to the cusp point. A conditional calculation of these groups was given earlier by Hesselholt, assuming a…
This article is devoted to the investigation of the deformation (twisting) of monoidal structures, such as the associativity constraint of the monoidal category and the monoidal structure of monoidal functor. The sets of twistings have a…
We present a framework for the computation of the Hopf 2-cocycles involved in the deformations of Nichols algebras over semisimple Hopf algebras. We write down a recurrence formula and investigate the extent of the connection with invariant…
A hom-associative algebra is an algebra whose associativity is twisted by an algebra homomorphism. It was previously shown by the author that the Hochschild cohomology of a hom-associative algebra $A$ carries a Gerstenhaber structure. In…
In this note, we extend the theory of Chern-Cheeger-Simons to construct canonical invariants for a one-parameter family of flat connections on a smooth manifold. These invariants lie in degrees $(2p-2)$-cohomology with $\C/\Z$-cohomology,…
The primary interest of this paper is to discuss the role of twisting cochains in the theory of characteristic classes. We begin with the homological description of monodromy map, associated with a connection on a trivial bundle over a…
We prove finite generation of the cohomology ring of any finite dimensional pointed Hopf algebra, having abelian group of grouplike elements, under some mild restrictions on the group order. The proof uses the recent classification by…
We introduce $k$-robust clique complexes, a family of simplicial complexes that generalizes the traditional clique complex. Here, a subset of vertices forms a simplex provided it does not contain an independent set of size $k$. We…
Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…
A chain complex model for the free loop space of a connected, closed and oriented manifold is presented, and on its homology, the Gerstenhaber and Batalin-Vilkovisky algebra structures are defined and identified with the string topology…
We describe the Gerstenhaber algebra structure on the Hochschild cohomology HH*$(A)$ when $A$ is a quadratic string algebra. First we compute the Hochschild cohomology groups using Barzdell's resolution and we describe generators of these…
This is a contribution to the classification of finite-dimensional Hopf algebras over an algebraically closed field $\Bbbk$ of characteristic 0. Concretely, we show that a finite-dimensional Hopf algebra whose Hopf coradical is basic is a…
We obtain a decomposition for the Hochschild cochain complex of a split algebra and we study some properties of the cohomology of each term of this decomposition. Then, we consider the case of trivial extensions, specially of Frobenius…
In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^\delta\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat…
Building on the recent determination of the simplicial cohomology groups of the convolution algebra ${\ell}^1({\mathbb Z}_+^k)$ [Gourdeau, Lykova, White, 2005] we investigate what can be said for cohomology of this algebra with more general…