Stable Type of the Mapping Class Group

Abstract

We use dynamics of the Teichm$\ddot{\mathrm{u}}$ller geodesic flow to show that the action of the mapping class group on the space of projective measured foliations has stable type $II{I}_{\lambda }$ for some $\lambda >0$. We do this by generalizing a criterion due to Bowen for a number to be in the stable ratio set, and proving some Patterson-Sullivan type results for the Thurston measure on $PMF$.

References in corpus (2)

• Lattice Point Asymptotics and Volume Growth on Teichmuller space
• Statistical hyperbolicity in Teichmüller space