On the Baum-Connes conjecture in the real case
Operator Algebras
2016-09-07 v1 K-Theory and Homology
Abstract
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.
Cite
@article{arxiv.math/0509495,
title = {On the Baum-Connes conjecture in the real case},
author = {Paul Baum and Max Karoubi},
journal= {arXiv preprint arXiv:math/0509495},
year = {2016}
}
Comments
5 pages, see also http://www.math.jussieu.fr/~karoubi/