Stable cubulations, bicombings, and barycenters

Matthew Gentry Durham, Yair N. Minsky, Alessandro Sisto

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
46 Downloads (Pure)


We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichmüller spaces are stably approximated by CAT(0) cube complexes, strengthening a result of Behrstock, Hagen and Sisto. As applications, we prove that mapping class groups are semihyperbolic and Teichmüller 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.
Original languageEnglish
Pages (from-to)2383–2478
Number of pages96
JournalGeometry and Topology
Issue number6
Publication statusPublished - 25 Aug 2023


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