Stable cubulations, bicombings, and barycenters
arXiv:2009.13647 · doi:10.2140/gt.2023.27.2383
Abstract
We prove that the hierarchical hulls of finite sets of points in mapping class groups and Teichmüller 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 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.
arXiv comment80 pages, 25 figures
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Cited by in corpus (4)
- Coarse injectivity, hierarchical hyperbolicity, and semihyperbolicity
- Extensions of Veech groups II: Hierarchical hyperbolicity and quasi-isometric rigidity
- The mapping class group of a nonorientable surface is quasi-isometrically embedded in the mapping class group of the orientation double cover
- A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces