相关论文: Equivariant Coarse (Co-)Homology Theories

We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the…

The results of a previous paper on the equivariant homotopy theory of crossed complexes are generalised from the case of a discrete group to general topological groups. The principal new ingredient necessary for this is an analysis of…

We provide and study an equivariant theory of group (co)homology of a group G with coefficients in a gamma-equivariant G-module A, when a separate group "gamma" acts on G and A, generalizing the classical Eilenberg-MacLane (co)homology of…

We propose an axiomatic characterization of coarse homology theories defined on the category of bornological coarse spaces. We construct a category of motivic coarse spectra. Our focus is the classification of coarse homology theories and…

For a $C^{*}$-category with a strict $G$-action we construct examples of equivariant coarse homology theories. To this end we first introduce versions of Roe categories of objects in $C^{*}$-categories which are controlled over bornological…

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…

We begin the study the algebraic topology of semi-coarse spaces, which are generalizations of coarse spaces that enable one to endow non-trivial `coarse-like' structures to compact metric spaces, something which is impossible in coarse…

In this paper, we construct an equivariant coarse homology theory with values in the category of non-commutative motives of Blumberg, Gepner and Tabuada, with coefficients in any small additive category. Equivariant coarse K-theory is…

In this monograph we lay the foundation for a theory of coarse groups and coarse actions. Coarse groups are group objects in the category of coarse spaces, and can be thought of as sets with operations that satisfy the group axioms "up to…

In this article we study the equivariant elliptic cohomology of complex toric varieties. We prove a partial reconstruction theorem showing that equivariant elliptic cohomology encodes considerable non-trivial information on the equivariant…

We present a version of higher Hochschild homology for spaces equipped with principal bundles for a structure group $G$. As coefficients, we allow $E_\infty$-algebras with $G$-action. For this homology theory, we establish an equivariant…

Given an action of a Lie group on a smooth manifold, we discuss the induced action on the Hochschild cohomology of smooth functions, and notions of invariance on this space. Depending on whether one considers invariance of cochains or…

We generalize some of the fundamental results of algebraic topology from topological spaces to \v{C}ech's closure spaces, also known as pretopological spaces. Using simplicial sets and cubical sets with connections, we define three distinct…

We introduce a new cohomology theory for stacks called elliptic Hochschild homology, prove some fundamental properties and compute it in some classes of examples. We then introduce its periodic cyclic version and show that, over the complex…

We introduce the notion of \emph{topo-symmetric extensions} of topological groups, a new generalization of classical group extensions that incorporates both topological and symmetry constraints. We define morphisms between such extensions,…

Equivariant cohomology is a mathematical framework particularly well adapted to a kinematical understanding of topological gauge theories of the cohomological type. It also sheds some light on gauge fixing, a necessary field theory…

To a coarse structure we associate a Grothendieck topology which is determined by coarse covers. A coarse map between coarse spaces gives rise to a morphism of Grothendieck topologies. This way we define sheaves and sheaf cohomology on…

For every strong coarse homology theory we construct a coarse assembly map as a natural transformation between coarse homology theories. We provide various conditions implying that this assembly map is an equivalence. These results…

Using the language of coarse homology theories, we provide an axiomatic account of vanishing results for the fibres of forget-control maps associated to spaces with equivariant finite decomposition complexity.

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin and W. Graham. It is based on lectures…