Speaker: Jason Behrstock,University of Utah
Title of talk: Dimension and rank of mapping classgroups
Abstract: We will discuss recent work withYair Minsky towards understanding the large scale geometry of themapping class group. In particular, we'll explain how to obtain varioustopological properties of the asymptotic cone of the mapping classgroup including a computation of its dimension. An application of thisanalysis is an affirmative solution to Brock-Farb's Rank Conjecturewhich asserts that MCG has quasi-flats of dimension N if and only if ithas a rank N free abelian subgroup. Applications to the study ofTeichmuller space will also be mentioned.