On the Baum-Connes conjecture in the real case

Details On the Baum-Connes conjecture in the real case On the Baum-Connes conjecture in the real case

2005-09-21

arxiv.org/abs/math/0509495v1

Q. J. Math, Vol. 55 (3) (2004) 231-235

Mathematics

Operator Algebras

5 pages, see also http://www.math.jussieu.fr/~karoubi/

Scientific paper

We prove that if the classical Baum-Connes conjecture in complex K-theory is true (for a given discrete group G), then the conjecture is also true in the real case (for the same group G). The essential ingredients of the proof are the descent theorem in topological K-theory (math.KT/0509396) and a Paschke duality for C*-algebras proved by John Roe (Q.J. Math. 55 (2004) 325-331). According to S. Stolz, this result is linked with the existence of a Riemannian metric of positive scalar curvature on a compact connected spin manifold with G as fundamental group.

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