Bicombing the mapping class group and Teichmüller space via stable cubical intervals
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914227048939520 |
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| author | Durham, Matthew Gentry |
| author_facet | Durham, Matthew Gentry |
| contents | In this mostly expository article, we provide a new account of our proof with Minsky and Sisto that mapping class groups and Teichmüller spaces admit bicombings. More generally, we explain how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension, with the added property that perturbing the pair of points results in a uniformly bounded change to the cubical structure. Our approach is simplified and new in many aspects. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_24136 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bicombing the mapping class group and Teichmüller space via stable cubical intervals Durham, Matthew Gentry Geometric Topology Group Theory Metric Geometry 20F67, 20F65, 30F60, 57M60, 57M07 In this mostly expository article, we provide a new account of our proof with Minsky and Sisto that mapping class groups and Teichmüller spaces admit bicombings. More generally, we explain how the hierarchical hull of a pair of points in any colorable hierarchically hyperbolic space is quasi-isometric to a finite CAT(0) cube complex of bounded dimension, with the added property that perturbing the pair of points results in a uniformly bounded change to the cubical structure. Our approach is simplified and new in many aspects. |
| title | Bicombing the mapping class group and Teichmüller space via stable cubical intervals |
| topic | Geometric Topology Group Theory Metric Geometry 20F67, 20F65, 30F60, 57M60, 57M07 |
| url | https://arxiv.org/abs/2512.24136 |