Topological equivariant coarse K-homology

Abstract

For a $C^{\ast }$-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 $C^{\ast }$-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.

arXiv comment79p, revised version

References in corpus (14)

• Higher Topos Theory
• The K-theoretic Farrell-Jones Conjecture for hyperbolic groups
• Coarse homology theories
• Equivariant coarse homotopy theory and coarse algebraic $\mathbf{K}$-homology
• Split injectivity of A-theoretic assembly maps
• Transfers in coarse homology
• On bicolimits of $C^{\ast }$-categories
• Generalized bornological coarse spaces and coarse motivic spectra
• Controlled objects in left-exact $\infty$-categories and the Novikov conjecture
• Injectivity results for coarse homology theories
• Equivariant Coarse (Co-)Homology Theories
• An identification of the Baum-Connes and Davis-Lück assembly maps
• Additive C*-categories and K-theory
• Homotopy theory with marked additive categories

Cited by in corpus (4)

• The coarse index class with support
• Localization for coarse homology theories
• Paschke duality and assembly maps
• A stable $\infty$-category for equivariant $KK$-theory