Counting pseudo-Anosovs as weakly contracting isometries
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912656162553856 |
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| author | Choi, Inhyeok |
| author_facet | Choi, Inhyeok |
| contents | We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous result for rank-one CAT(0) groups and hierarchically hyperbolic groups with Morse elements. Finally, we prove that Morse elements are generic in every Cayley graph of groups that are quasi-isometric to (well-behaved) hierarchically hyperbolic groups. This gives a quasi-isometry invariant theory of counting group elements in groups beyond relatively hyperbolic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_00603 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Counting pseudo-Anosovs as weakly contracting isometries Choi, Inhyeok Geometric Topology Group Theory We show that pseudo-Anosov mapping classes are generic in every Cayley graph of the mapping class group of a finite-type hyperbolic surface. Our method also yields an analogous result for rank-one CAT(0) groups and hierarchically hyperbolic groups with Morse elements. Finally, we prove that Morse elements are generic in every Cayley graph of groups that are quasi-isometric to (well-behaved) hierarchically hyperbolic groups. This gives a quasi-isometry invariant theory of counting group elements in groups beyond relatively hyperbolic groups. |
| title | Counting pseudo-Anosovs as weakly contracting isometries |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2408.00603 |