Coarse topology, enlargeability, and essentialness

Details Coarse topology, enlargeability, and essentialness Coarse topology, enlargeability, and essentialness

2007-07-13

arxiv.org/abs/0707.1999v2

Ann. Sci. Ecole Norm. Sup. 41 (2008), 471--493

Mathematics

Algebraic Topology

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

Scientific paper

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.

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