Equivariant Coarse (Co-)Homology Theories

  title={Equivariant Coarse (Co-)Homology Theories},
  author={Christopher Wulff},
  journal={Symmetry, Integrability and Geometry: Methods and Applications},
  • Christopher Wulff
  • Published 3 June 2020
  • Mathematics
  • Symmetry, Integrability and Geometry: Methods and Applications
We present an Eilenberg-Steenrod-like axiomatic framework for equivariant coarse homology and cohomology theories. We also discuss a general construction of such coarse theories from topological ones and the associated transgression maps. A large part of this paper is devoted to showing how some well-established coarse (co-)homology theories, whose equivariant versions are either already known or will be introduced in this paper, fit into this setup. Furthermore, a new and more flexible notion… 
3 Citations

Coarse sheaf cohomology

A certain Grothendieck topology assigned to a metric space gives rise to a sheaf cohomology theory which sees the coarse structure of the space. Already constant coefficients produce interesting

Secondary cup and cap products in coarse geometry

We construct secondary cup and cap products on coarse (co-)homology theories from given cross and slant products. They are defined for coarse spaces relative to weak generalized controlled

Topological equivariant coarse K-homology

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




We formulate and study a new coarse (co-)assembly map. It involves a modification of the Higson corona construction and produces a map dual in an appropriate sense to the standard coarse assembly


  • New Jersey,
  • 1952

Simultaneous metrizability of coarse spaces

A metric space can be naturally endowed with both a topology and a coarse structure. We examine the converse to this. Given a topology and a coarse structure we give necessary and sufficient

Homotopy Theory with Bornological Coarse Spaces

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

Coarse and equivariant co-assembly maps

We study an equivariant co-assembly map that is dual to the usual Baum-Connes assembly map and closely related to coarse geometry, equivariant Kasparov theory, and the existence of dual Dirac


  • 5(2):161–186,
  • 2006

Comparing Analytic Assembly Maps

C*-Algebras and Controlled Topology

This paper is an attempt to explain some aspects of the relationship between the K-theory of C-algebras, on the one hand, and the categories of modules that have been developed to systematize the

Cambridge Studies in Advanced Mathematics

  • Cambridge University Press,
  • 2020