Geometry of the mapping class groups III: Quasi-isometric rigidity

Details Geometry of the mapping class groups III: Quasi-isometric rigidity Geometry of the mapping class groups III: Quasi-isometric rigidity

2005-12-18

arxiv.org/abs/math/0512429v2

Mathematics

Geometric Topology

73 p, 7 figures. Completely rewritten. Substantial corrections. Proof of quasi-isometric rigidity added

Scientific paper

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.

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