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

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.

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

References in corpus (1)

• Dimension and rank for mapping class groups

Cited by in corpus (10)

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• The geometry of the curve graph of a right-angled Artin group
• Automorphisms of contact graphs of $\mathrm{CAT}(0)$ cube complexes
• Rigidity of mapping class groups mod powers of twists
• Large-scale geometry of the saddle connection graph
• Asymptotic Dimension of Big Mapping Class Groups