The Novikov conjecture and groups with finite asymptotic dimension, by Guoliang Yu

In this paper we prove the coarse Baum-Connes conjecture for proper metric spaces with finite asymptotic dimension. As applications we obtain the following:

(1) The Novikov conjecture holds for finitely generated groups with finite asymptotic dimension and whose classifying spaces are of finite homotopy type;

(2) Gromov's zero-in-the-spectrum conjecture for uniformly contractible Riemannian manifolds holds for Riemannian manifolds with finite asymptotic dimension;

(3) A uniformly contractible Riemannian manifold cannot have uniform positive scalar curvature.

This paper has appeared in Annals of Math, Vol. 147, 2 (1998), 325-355.


Guoliang Yu <gyu@euclid.colorado.edu>