4/15/2004
Bernhard Hanke
Universitat Muenchen
Enlargeability and Index Theory
Abstract
Let M be a smooth, compact enlargeable spin manifold. Independently of the Baum-Connes conjecture, we prove nonvanishing of a universal index obstruction associated witn M. This implies the result by Gromov and Lawson that M does not admit a metric of positive scalar curvature. As an application of our methods we show that the map --> B\pi_1(M) classifying the universal cover of M sends the fundamental homology class of M to a non trivial class in H_*(B\pi_1(M); Q. This answers a question of D. Burghelea (1983).