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"

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"

## Date:

Thu, 10/12/2015 - 10:00 to 11:00

## Location:

Ross building, Hebrew University of Jerusalem, (Room 70)