Algebraic & Geometric Topology 4 (2004) 333–346

DOI: 10.2140/agt.2004.4.333

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

Primary: 19K35, 55N15

References

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Publication

Received: 24 November 2003
Accepted: 29 May 2004
Published: 29 May 2004

Authors