Volume 4, issue 1 (2004)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Real versus complex K–theory using Kasparov's bivariant KK–theory

Thomas Schick

Algebraic & Geometric Topology 4 (2004) 333–346

arXiv: math.KT/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
real $K$–theory, complex $K$–theory, bivariant $K$–theory
Mathematical Subject Classification 2000
Primary: 19K35, 55N15
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Publication
Received: 24 November 2003
Accepted: 29 May 2004
Published: 29 May 2004
Authors
Thomas Schick
Fachbereich Mathematik
Georg-August-Universität Göttingen
Germany
http://www.uni-math.gwdg.de/schick/