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

Ursula Hamenstaedt

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

Ursula Hamenstaedt

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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.

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Ursula Hamenstaedt. 2007-01-28. Geometry of the mapping class groups III: Quasi-isometric rigidity. https://arxiv.org/abs/math/0512429

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