Pseudo-Anosovs are exponentially generic in mapping class groups
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arXiv
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866914881682276352 |
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| author | Choi, Inhyeok |
| author_facet | Choi, Inhyeok |
| contents | Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of radius $R$ decrease to 0 as $R$ increases? We show that any finite subset $S'$ of the mapping class group is contained in a finite generating set $S$ such that this proportion decreases exponentially. Our strategy applies to weakly hyperbolic groups and does not refer to the automatic structure of the group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_06678 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Pseudo-Anosovs are exponentially generic in mapping class groups Choi, Inhyeok Geometric Topology Group Theory Given a finite generating set $S$, let us endow the mapping class group of a closed hyperbolic surface with the word metric for $S$. We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of radius $R$ decrease to 0 as $R$ increases? We show that any finite subset $S'$ of the mapping class group is contained in a finite generating set $S$ such that this proportion decreases exponentially. Our strategy applies to weakly hyperbolic groups and does not refer to the automatic structure of the group. |
| title | Pseudo-Anosovs are exponentially generic in mapping class groups |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2110.06678 |