The asymptotic geometry of the Teichmüller metric: Dimension and rank

Abstract

We analyze the asymptotic cones of Teichmüller space with the Teichmüller metric, $(\mathcal{T}(S),d_T)$. We give a new proof of a theorem of Eskin-Masur-Rafi which bounds the dimension of quasiisometrically embedded flats in $(\mathcal{T}(S),d_T)$. Our approach is an application of the ideas of Behrstock and Behrstock-Minsky to the quasiisometry model we previously built for $(\mathcal{T}(S),d_T)$.

16 pages