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Coarse homology theories

Paul D Mitchener

Algebraic & Geometric Topology 1 (2001) 271–297

arXiv: math.AT/0106183

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.

Keywords
coarse geometry, exotic homology, coarse Baum–Connes conjecture, Novikov conjecture
Mathematical Subject Classification 2000
Primary: 55N35, 55N40
Secondary: 19K56, 46L85
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Publication
Received: 12 February 2001
Revised: 10 May 2001
Accepted: 16 May 2001
Published: 22 May 2001
Authors
Paul D Mitchener
Department of Mathematics and Computer Science
Odense University
Denmark
http://www.imada.sdu.dk/~mitchene/index2.html