Related papers: A spectral sequence in Bredon cohomology

We construct a multiplicative spectral sequence converging to the cohomology algebra of the diagonal complex of a bisimplicial set with coefficients in a field. The construction provides a spectral sequence converging to the cohomology…

Let $G$ be a group and $S$ a unital epsilon-strongly $G$-graded algebra. We construct spectral sequences converging to the Hochschild (co)homology of $S$. Each spectral sequence is expressed in terms of the partial group (co)homology of $G$…

For a topological space $X$, we introduce a criterion for the $\rm FI$ module $H^i({\rm Conf}_n(X))$ to be finitely generated and give several applications. For instance, if $C$ is a finite connected $CW$ complex, then $X = C \times…

We are interested in computing the Bredon cohomology with coefficients in the constant Mackey functor $\underline{ \mathbb{F}_2}$ for equivariant $\text{Rep}(C_2)$ spaces, in particular for Grassmannian manifolds of the form…

We obtain the equivariant K-homology of the classifying space \underline{E}W for W a right-angled or, more generally, an even Coxeter group. The key result is a formula for the relative Bredon homology of \underline{E}W in terms of Coxeter…

Let {X_i} be a tower of discrete G-spectra, each of which is fibrant as a spectrum, so that X=holim_i X_i is a continuous G-spectrum, with homotopy fixed point spectrum X^{hG}. The E_2-term of the descent spectral sequence for \pi_*(X^{hG})…

The aim of this paper is to introduce and study a geometric spectral sequence in Khovanov homology. The construction was motivated by a similar spectral sequence from Khovanov homology to Heegaard Floer homology.

Stefan and Guichardet have provided Lyndon-Hochschild-Serre type spectral sequences which converge to the Hochschild cohomology and Ext groups of a smash product. We show that these spectral sequences carry natural multiplicative…

Locally trivial bundles of $C^*$-algebras with fibre $D \otimes \mathcal{K}$ for a strongly self-absorbing $C^*$-algebra $D$ over a finite CW-complex $X$ form a group $E^1_D(X)$ that is the first group of a cohomology theory $E^*_D(X)$. In…

In this paper, we construct a seven-term exact sequence involving the cohomology groups of a group extension. Although the existence of such a sequence can be derived using spectral sequence arguments, there is little knowledge about some…

We consider the change-of-rings spectral sequence as it applies to Hochschild cohomology, obtaining a description of the differentials on the first page which relates it to the multiplicative stucture on cohomology. Using this information,…

We give a direct description of the category of sheaves on Lichtenbaum's Weil-\'etale site of a number ring. Then we apply this result to define a spectral sequence relating Weil-\'etale cohomology to Artin-Verdier \'etale cohomology.…

Let G be an algebraic group and let X be a smooth integral scheme over a field k. In this paper we construct homology-type groups $H_i(X,G)$ by considering cycles in the simplicial scheme $BG\times X (an idea suggested by Andrei Suslin). We…

We prove simplicial version of a classical theorem of Eilenberg in the equivariant context and give an alternative description of the simplicial version of Bredon-Illman cohomology with local coefficients, as introduced in [15], to derive a…

We introduce a new spectral sequence called the p-chain spectral sequence which converges to the (co-)homology of a contravariant C-space with coefficients in a covariant C-spectrum for a small category C. It is different from the…

A careful account is given of generalized equivariant homology theories on the category of topological pairs acted on by a group. In particular, upon restriction to the category of equivariant simplicial complexes, the equivalence of…

Over the complex numbers, we compute the $C_2$-equivariant Bredon motivic cohomology ring with $\mathbb{Z}/2$ coefficients. By rigidity, this extends Suslin's calculation of the motivic cohomology ring of algebraically closed fields of…

We introduce the notion of a Bredon-style equivariant coarse homology theory. We show that such a Bredon-style equivariant coarse homology theory satisfies localization theorems and that a general equivariant coarse homology theory can be…

In this paper the authors investigate the structure of the Hochschild cohomology for Frobenius kernels. The authors first establish some fundamental constructions to compute Hochschild cohomology by using spectral sequences. This enables us…

In this work, we construct a persistent version of the well-known Leray spectral sequence. More precisely, we construct a spectral sequence that computes the persistent cohomology of a space from the persistent cohomology in each open set…