Coarse homology theories

2001/06/21 by Paul D. Mitchener · 2 citations
Mathematics · #math.AT #msc:55N35 #msc:55N40 #msc:19K56 #msc:46L85

paper · pdf · doi:10.2140/agt.2001.1.271

published as Algebr. Geom. Topol. 1 (2001) 271-297 · Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-13.abs.html

arxiv created 2001/06/21 · arxiv updated 2014/09/30

Abstract

In this paper we develop an axiomatic approach to coarse homology theories. We prove a uniqueness result concerning coarse homology theories on the category of `coarse CW-complexes'. This uniqueness result is used to prove a version of the coarse Baum-Connes conjecture for such spaces.

Cited by

• Quantum cellular automata are a coarse homology theory
• Coarse Baum-Connes and warped cones: failure of surjectivity in odd degree