Dimension and rank for mapping class groups

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dc.creatorBehrstock, Jason A.
dc.creatorMinsky, Yair N.
dc.date2005-12-15
dc.date2007-01-12
dc.date.accessioned2026-07-07T10:18:11Z
dc.date.available2026-07-07T10:18:11Z
dc.descriptionWe study the large scale geometry of the mapping class group, MCG. Our main result is that for any asymptotic cone of MCG, the maximal dimension of locally compact subsets coincides with the maximal rank of free abelian subgroups of MCG. An application is an affirmative solution to Brock-Farb's Rank Conjecture which asserts that MCG has quasi-flats of dimension N if and only if it has a rank N free abelian subgroup. We also compute the maximum dimension of quasi-flats in Teichmuller space with the Weil-Petersson metric.
dc.descriptionIncorporates referee's suggestions. To appear in Annals of Mathematics
dc.identifierhttps://arxiv.org/abs/math/0512352
dc.identifierhttp://arxiv.org/abs/math/0512352
dc.identifierAnnals of Math, 167, (2008), 1055-1077
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/174108
dc.subjectGeometric Topology
dc.subjectGroup Theory
dc.subject20F65, 57M50
dc.titleDimension and rank for mapping class groups
dc.typetext

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