Patterson-Sullivan Theory for Subgroups of Mapping Class
Groups and Orbit Counting in Teichmuller Space
Ilya Gekhtman (University of Chicago)
Abstract: We develop an analogue of Patterson-Sullivan theory
for convex-cocompact subgroups of mapping class groups acting on
the sphere of projective measured foliations, and use it to
compute exact multiplicative asymptotics for orbit growth of
such groups in Teichmueller space and growth of conjugacy
classes of Pseudo-Anosovs of such groups with bounded
dilatation. The methods rely on controlling areas in TeichmuIler
space where negative curvature fails.