Real versus complex K-theory using Kasparov's bivariant KK-theory

Preprint

2 June 2004

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0311295

Abstract

In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the Baum-Connes conjecture for a discrete group to its complex counterpart. In particular, the complex Baum-Connes assembly map is an isomorphism if and only if the real one is, thus reproving a result of Baum and Karoubi. After inverting 2, the same is true for the injectivity or surjectivity part alone.

Keywords

KASPAROV'S BIVARIANT
USING KASPAROV'S
BIVARIANT KK
KK THEORY
COMPLEX K
K THEORY
ALGEBRA
BAUM

All Related Versions

Version 1, 2003-11-17, ArXiv
Version 2, 2003-11-24, ArXiv
Version 3, 2004-06-02, ArXiv
Published version: Algebraic & Geometric Topology, 4 (1), 333.

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