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Stable cubulations, bicombings, and barycenters

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arxiv 2009.13647 v1 pith:43OHRBQI submitted 2020-09-28 math.GR math.GTmath.MG

Matthew G. Durham , Yair N. Minsky , Alessandro Sisto This is my paper · ORCID
classification math.GRmath.GTmath.MG
keywords classgroupsspacesbarycentersmappingprovestableteichm
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We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichm\"uller spaces are stably approximated by a CAT(0) cube complexes, strengthening a result of Behrstock-Hagen-Sisto. As applications, we prove that mapping class groups are semihyperbolic and Teichm\"uller spaces are coarsely equivariantly bicombable, and both admit stable coarse barycenters. Our results apply to the broader class of "colorable" hierarchically hyperbolic spaces and groups.

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  1. The geometry of totally geodesic subvarieties of moduli spaces of Riemann surfaces

    math.GT 2024-12 conditional novelty 8.0 of 10

    Totally geodesic subvarieties of moduli space have semisimple Deligne-Mumford boundary and are hierarchically hyperbolic.

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