Abstract

Patterson-Sullivan Theory for Subgroups of Mapping Class Groups and Orbit Growth in Teichmüller Space

Ilya Gekhtman
University of Chicago
Mathematics

For a convex cocompact subgroup $G< Mod(S)$ of a mapping class group we construct an analogue of the Bowen-Margulis measure on $Q^1(S)/G$, show that it is mixing, and use this to compute precise multiplicative asymptotics for orbit growth of $G$ in the Teichmüller metric.