Algebraic & Geometric Topology

Coarse homology theories

Paul D Mitchener

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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.

Article information

Source
Algebr. Geom. Topol., Volume 1, Number 1 (2001), 271-297.

Dates
Received: 12 February 2001
Revised: 10 May 2001
Accepted: 16 May 2001
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882593

Digital Object Identifier
doi:10.2140/agt.2001.1.271

Mathematical Reviews number (MathSciNet)
MR1834777

Zentralblatt MATH identifier
0978.58011

Subjects
Primary: 55N35: Other homology theories 55N40: Axioms for homology theory and uniqueness theorems
Secondary: 19K56: Index theory [See also 58J20, 58J22] 46L85: Noncommutative topology [See also 58B32, 58B34, 58J22]

Keywords
coarse geometry exotic homology coarse Baum–Connes conjecture Novikov conjecture

Citation

Mitchener, Paul D. Coarse homology theories. Algebr. Geom. Topol. 1 (2001), no. 1, 271--297. doi:10.2140/agt.2001.1.271. https://projecteuclid.org/euclid.agt/1513882593


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