Colloquium - Grigori Avramidi

Date: February 10, 2017

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Grigori Avramidi

Description:

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 less than dim M/2. In this talk, I will give examples illustrating this, and then I will explain aspects of the locally symmetric situation that are true for more general nonpositively curved manifolds. The main result is that the homology of the thin part of the universal cover vanishes in dimension greater or equal to dim M/2. One application is that any complex homotopy eqiuvalent to M has dimension greater or equal to dim M/2.