Large scale rank of Teichmuller space
Geometric Topology
2017-10-18 v2
Abstract
Let X be quasi-isometric to either the mapping class group equipped with the word metric, or to Teichmuller space equipped with either the Teichmuller metric or the Weil-Petersson metric. We introduce a unified approach to study the coarse geometry of these spaces. We show that the quasi-Lipschitz image in X of a box in R^n is locally near a standard model of a flat in X. As a consequence, we show that, for all these spaces, the geometric rank and the topological rank are equal. The methods are axiomatic and apply to a larger class of metric spaces.
Keywords
Cite
@article{arxiv.1307.3733,
title = {Large scale rank of Teichmuller space},
author = {Alex Eskin and Howard Masur and Kasra Rafi},
journal= {arXiv preprint arXiv:1307.3733},
year = {2017}
}
Comments
Some corrections have been made. Also, the coarse differentiation statement has been modified to state that a quasi-Lipschitz map is "differentiable almost everywhere"