Algebraic and Geometric Topology 1 (2001), paper no. 13, pages 271-297.

Coarse homology theories

Paul D. Mitchener

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

AMS subject classification. Primary: 55N35, 55N40. Secondary: 19K56, 46L85.

DOI: 10.2140/agt.2001.1.271

E-print: arXiv:math.AT/0106183

Submitted: 12 February 2001. (Revised: 10 May 2001.) Accepted: 16 May 2001. Published: 22 May 2001.

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Paul D. Mitchener
Department of Mathematics and Computer Science, Odense University, Denmark
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