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.