Localization for coarse homology theories

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.

48 pages, some typos corrected

References in corpus (7)

• Higher Topos Theory
• Models of G-spectra as presheaves of spectra
• Equivariant coarse homotopy theory and coarse algebraic $\mathbf{K}$-homology
• The coarse index class with support
• Topological equivariant coarse K-homology
• An identification of the Baum-Connes and Davis-Lück assembly maps
• Controlled objects as a symmetric monoidal functor

Cited by in corpus (2)

• The coarse index class with support
• Controlled objects as a symmetric monoidal functor