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Stable cubulations,
bicombings, and barycenters
Matthew G Durham, Yair N Minsky and Alessandro Sisto |
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Geometry & Topology 27 (2023) 2383–2478
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Abstract |
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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. |
Keywords
semihyperbolic, bicombing, mapping class group,
hierarchically hyperbolic, cube complexes, Teichmüller
space
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Mathematical Subject Classification
Primary: 20F65, 57K20
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References |
Publication
Received: 3 June 2021
Revised: 11 November 2021
Accepted: 12 December 2021
Published: 25 August 2023
Proposed: Mladen Bestvina
Seconded: David Fisher, Benson Farb
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Authors |
| Matthew G Durham | |
| Department of Mathematics University of California Riverside Riverside, CA United States |
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| Yair N Minsky | |
| Department of Mathematics Yale University New Haven, CT United States |
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| Alessandro Sisto | |
| Department of Mathematics Heriot-Watt University Edinburgh United Kingdom |
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| © 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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