Equivariant Coarse (Co-)Homology Theories

Christopher Wulff

Symmetry, integrability and geometry: methods and applications, Tome 18 (2022)

Résumé

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 of coarse homotopy is given which is more in the spirit of topological homotopies. Some, but not all, coarse (co-)homology theories are even invariant under these new homotopies. They also led us to a meaningful concept of topological actions of locally compact groups on coarse spaces.

Détail

Keywords: equivariant coarse homology, equivariant coarse cohomology, equivariant coarse assembly, equivariant coarse coassembly, generalized coarse homotopies.

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