Geometry of the mapping class groups III: Quasi-isometric rigidity
Geometric Topology
2007-05-23 v2 Group Theory
Abstract
Let S be an oriented surface of finite type of genus g with m punctures and where 3g-3+m>1. We show that the mapping class group M(S) of S is quasi-isometrically rigid. We also give a different proof of the following result of Behrstock and Minsky: The homological dimension of the asmyptotic cone of M(S) of S equals 3g-3+m.
Cite
@article{arxiv.math/0512429,
title = {Geometry of the mapping class groups III: Quasi-isometric rigidity},
author = {Ursula Hamenstaedt},
journal= {arXiv preprint arXiv:math/0512429},
year = {2007}
}
Comments
73 p, 7 figures. Completely rewritten. Substantial corrections. Proof of quasi-isometric rigidity added