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2004 Real versus complex K–theory using Kasparov's bivariant KK–theory
Thomas Schick
Algebr. Geom. Topol. 4(1): 333-346 (2004). DOI: 10.2140/agt.2004.4.333

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.

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Thomas Schick. "Real versus complex K–theory using Kasparov's bivariant KK–theory." Algebr. Geom. Topol. 4 (1) 333 - 346, 2004. https://doi.org/10.2140/agt.2004.4.333

Information

Received: 24 November 2003; Accepted: 29 May 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1050.19003
MathSciNet: MR2077669
Digital Object Identifier: 10.2140/agt.2004.4.333

Subjects:
Primary: 19K35, 55N15

Rights: Copyright © 2004 Mathematical Sciences Publishers

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