EVENT DETAILS AND ABSTRACT

Title: Compact forms of homogeneous spaces and group actions
Speaker: Dave Constantine
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

Given a homogeneous space J\H, does there exist a discrete subgroup \Gamma in H such that J\H/Gamma is a compact manifold? These compact forms of homogeneous spaces turn out to be rare outside of a few natural cases. Their existence has been studied by a very wide range of techniques, one of which is via the action of the centralizer of J in H. In this talk I'll show that no compact form exists when H is a simple Lie group, J is reductive and the acting group is higher-rank and semisimple. The proof uses cocycle superrigidity, Ratner's theorem and techniques from partially hyperbolic dynamics.