Asymptotic dimension of mapping class groups

03/23/2016 - 16:00
03/23/2016 - 17:00
Jason Behrstock, City University of New York
Burnside Hall, Room 920, McGill University

The goal of this talk will be to describe our recent result proving that the asymptotic dimension of the mapping class group of a closed surface is at most quadratic in the genus (building on and strengthening a prior result of Bestvina-Bromberg giving an exponential estimate). We obtain this result as a special case of a result about the asymptotic dimension of a general class of spaces, which we call hierarchically hyperbolic; this class includes hyperbolic spaces, mapping class groups, Teichmueller spaces endowed with either the Teichmuller or the Weil-Petersson metric, fundamental groups of non-geometric 3-manifolds, RAAGs, etc. We will discuss the general framework and a sketch of how this machinery provides new tools for studying special subclasses, such as mapping class groups. The results discussed are joint work with Mark Hagen and Alessandro Sisto.

Last edited by on Thu, 03/17/2016 - 13:29