Geometry, Topology and Dynamics Seminar
David Constantine
University of Chicago
Compact forms of homogeneous spaces and group actions
Abstract: A compact Clifford-Klein form of the homogeneous space $J\backslash H$ is constructed by finding a discrete subgroup $\Gamma$ in $H$ such that $J\backslash H/\Gamma$ is a compact manifold.
The question of which homogeneous spaces admit compact forms is an extensive one which has been studied using a wide variety of techniques.
In this talk I'll discuss an approach which uses Zimmer's cocycle superrigidity to prove non-existence of some compact forms admitting higher-rank semisimple group actions.
The proof uses Ratner's theorems on unipotent flows and some ideas from measure rigidity for abelian actions as well.
Monday March 14, 2011 at 3:00 PM in SEO 636