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Topological equivariant coarse $K\mkern-2mu$-homology

Ulrich Bunke and Alexander Engel

Vol. 8 (2023), No. 2, 141–220
Abstract

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 coarse spaces, and then apply a homological functor. These equivariant coarse homology theories are then employed to verify that certain functors on the orbit category are CP-functors. This fact has consequences for the injectivity of assembly maps.

Keywords
coarse homology, $K\mkern-2mu$-theory
Mathematical Subject Classification
Primary: 19K99, 46L80, 51F30
Milestones
Received: 10 February 2022
Revised: 10 April 2023
Accepted: 2 May 2023
Published: 14 June 2023
Authors
Ulrich Bunke
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany
Alexander Engel
Institut für Mathematik und Informatik
Universität Greifswald
Greifswald
Germany