Abstract: Borel studied the topological group actions that are possible on locally symmetric manifolds. In these two talks, I will explain Borel's work and interpret these results as a type of rigidity statement very much related to the well-known Borel conjecture of high dimensional topology. In particular, I will give the characterization of locally symmetric manifolds (of dimension not 4) which have a unique maximal conjugacy of finite group of orientation preserving homeomorphisms, due to Cappell, Lubotzky and myself. We will then discuss several sources of counterexamples to stronger rigidity statements, coming from either algebra or the theory of "nonlinear averaging of embeddings"
Thu, 03/12/2015 - 10:00 to 11:20
Ross building, Hebrew University of Jerusalem, (Room 70)