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Fall 2002 Mapping the homology of a group to the $K$-theory of its $C\sp *$-algebra
Michel Matthey
Illinois J. Math. 46(3): 953-977 (Fall 2002). DOI: 10.1215/ijm/1258130995

Abstract

For a CW-complex $X$ and for $0\leq j\leq 2$, we construct natural homomorphisms $\beta_{j}^{X}\colon H_{j}(X;\,\mathbb{Z}) \longrightarrow K_{j}(X)$ that are rationally right-inverses of the Chern character. We show that $\beta_{j}^{X}$ is injective for $j=0$ and $j=1$. The case $j=3$ is treated using $\mathbb{Z}[\frac12]$-coefficients. The study of these maps is motivated by the connection with the Baum-Connes conjecture on the $K$-theory of group $C^{*}$-algebras.

Citation

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Michel Matthey. "Mapping the homology of a group to the $K$-theory of its $C\sp *$-algebra." Illinois J. Math. 46 (3) 953 - 977, Fall 2002. https://doi.org/10.1215/ijm/1258130995

Information

Published: Fall 2002
First available in Project Euclid: 13 November 2009

zbMATH: 1021.19003
MathSciNet: MR1951251
Digital Object Identifier: 10.1215/ijm/1258130995

Subjects:
Primary: 19K56
Secondary: 19L10, 19L41, 55S45, 57R20

Rights: Copyright © 2002 University of Illinois at Urbana-Champaign

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Vol.46 • No. 3 • Fall 2002
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