Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866909450126753792 |
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| author | Goldsborough, Antoine Hagen, Mark Petyt, Harry Russell, Jacob Sisto, Alessandro |
| author_facet | Goldsborough, Antoine Hagen, Mark Petyt, Harry Russell, Jacob Sisto, Alessandro |
| contents | We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical hyperbolicity, and the other a linear progress result for Markov chains. The appendix, by Jacob Russell, contains a partial converse under the (necessary) condition that the maximal hyperbolic space is one-ended. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07013 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity Goldsborough, Antoine Hagen, Mark Petyt, Harry Russell, Jacob Sisto, Alessandro Group Theory Probability We show that quasi-isometries of (well-behaved) hierarchically hyperbolic groups descend to quasi-isometries of their maximal hyperbolic space. This has two applications, one relating to quasi-isometry invariance of acylindrical hyperbolicity, and the other a linear progress result for Markov chains. The appendix, by Jacob Russell, contains a partial converse under the (necessary) condition that the maximal hyperbolic space is one-ended. |
| title | Induced quasi-isometries of hyperbolic spaces, Markov chains, and acylindrical hyperbolicity |
| topic | Group Theory Probability |
| url | https://arxiv.org/abs/2309.07013 |