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Localization for coarse homology theories

Ulrich Bunke and Luigi Caputi

Vol. 9 (2024), No. 1, 41–88
Abstract

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 approximated by a Bredon-style version. We discuss the special case of algebraic and topological equivariant coarse K-homology and obtain the coarse analog of Segal’s localization theorem.

Keywords
coarse homology theory, localization, Bredon style homology
Mathematical Subject Classification
Primary: 55P91
Secondary: 19E20
Milestones
Received: 29 December 2022
Revised: 12 March 2024
Accepted: 1 April 2024
Published: 25 May 2024
Authors
Ulrich Bunke
Fakultät für Mathematik
Universität Regensburg
Regensburg
Germany
Luigi Caputi
Department of Mathematics
University of Bologna
Bologna
Italy