Algebraic and Geometric Topology 4 (2004), paper no. 18, pages 333-346.

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

Thomas Schick

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

AMS subject classification. Primary: 19K35, 55N15.

DOI: 10.2140/agt.2004.4.333

E-print: arXiv:math.KT/0311295

Submitted: 24 November 2003. Accepted: 29 May 2004. Published: 29 May 2004.

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Thomas Schick
Fachbereich Mathematik, Georg-August-Universitaet
Goettingen, Germany

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