# Dr. Tam Nguyen Phan, MPI Bonn: "Topology of ends of nonpositively curved manifolds"

Jan 30, 2020 from 04:15 PM to 05:45 PM

Abstract:

Locally symmetric manifolds of noncompact type form an interesting class of nonpositively curved manifolds. The topology of the end of a locally symmetric space is controlled by an arithmetically-constructed object called the "rational Tits building", which turns out to be homotopically a wedge of spheres of dimension q-1, where q is the "Q-rank" of the locally symmetric space. In general, q is less than or equal to half the dimension of the manifold. In joint work with Grigori Avramidi, we build a purely geometric analog of the rational Tits building for general noncompact, finite volume, complete, n-manifolds of bounded nonpositive curvature and use this to show that, loosely speaking, any topological feature that survives from being pushed to inﬁnity must be in dimension less than n/2. We also construct examples of such nonpositively cuved manifolds with mixed types of ends. This talk is about nonpositively curved geometry. No knowledge of Tits buildings is required (or will be given).