Title: Topology of ends of finite volume, nonpositively curved manifolds

Abstract: The structure of ends of a nonpositively curved, locally symmetric manifold M is very well understood. By Borel-Serre, the thin part of the universal cover of such a manifold is homotopy equivalent to a rational Tits building. This is a simplicial complex built out of the algebra of the locally symmetric space which turns out to have dimension = dim M/2.