Higher dimensional divergence for mapping class groups
Abstract
In this paper we investigate the higher dimensional divergence functions of mapping class groups of surfaces and of CAT(0)--groups. We show that, for mapping class groups of surfaces, these functions exhibit phase transitions at the rank (as measured by thrice the genus plus the number of punctures minus 3). We also provide inductive constructions of CAT(0)--spaces with co-compact group actions, for which the divergence below the rank is (exactly) a polynomial function of our choice, with degree arbitrarily large compared to the dimension.
Cite
@article{arxiv.1305.2994,
title = {Higher dimensional divergence for mapping class groups},
author = {Jason Behrstock and Cornelia Drutu},
journal= {arXiv preprint arXiv:1305.2994},
year = {2015}
}
Comments
Version 4: This version contains the applications to MCG and CAT(0) groups of higher divergence; setting up the framework with which we study these functions is now split into a separate paper by the same authors entitled "Combinatorial higher dimensional isoperimetry and divergence"