Coarse topology, enlargeability, and essentialness

Abstract

Using methods from coarse topology we show that fundamental classes of closed enlargeable manifolds map non-trivially both to the rational homology of their fundamental groups and to the K-theory of the corresponding reduced C*-algebras. Our proofs do not depend on the Baum--Connes conjecture and provide independent confirmation for specific predictions derived from this conjecture.

21 pages, 2 figures. Revised version. To appear in Ann. Sci. Ecole Norm. Sup