Equivariant coarse homotopy theory and coarse algebraic $\boldsymbol{K}$homology
Abstract
We study equivariant coarse homology theories through an axiomatic framework. To this end we introduce the category of equivariant bornological coarse spaces and construct the universal equivariant coarse homology theory with values in the category of equivariant coarse motivic spectra. As examples of equivariant coarse homology theories we discuss equivariant coarse ordinary homology and equivariant coarse algebraic $K$homology. Moreover, we discuss the cone functor, its relation with equivariant homology theories in equivariant topology, and assembly and forgetcontrol maps. This is a preparation for applications in subsequent papers aiming at splitinjectivity results for the FarrellJones assembly map.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 arXiv:
 arXiv:1710.04935
 Bibcode:
 2017arXiv171004935B
 Keywords:

 Mathematics  KTheory and Homology;
 Mathematics  Metric Geometry
 EPrint:
 110 pages, minor improvements