Geometry, Topology and Dynamics Seminar
Matthew Durham
UIC
Elliptic Actions on Teichmüller Space
Abstract: Kerckhoff's solution to the Nielsen realization problem showed that the action of any finite subgroup of the mapping class group on Teichmüller space has a fixed point. The set of fixed points is a totally geodesic submanifold. We study the coarse geometry of the set of points which have bounded diameter orbits in the Teichmüller metric. We show that each such almost-fixed point is within a uniformly bounded distance of the fixed point set, but that the set of almost-fixed points is not quasiconvex. In addition, the orbit of any point is shown to have a fixed barycenter. In this talk, I will discuss the machinery and ideas used in the proofs of these theorems.
Monday March 3, 2014 at 3:00 PM in SEO 636