Pseudo-Anosovs are exponentially generic in mapping class groups

Inhyeok Choi

doi:10.2140/gt.2024.28.1923

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arXiv · 2110.06678

Pseudo-Anosovs are exponentially generic in mapping class groups

Inhyeok Choi

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Abstract

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.

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BibTeX RIS

Inhyeok Choi. 2021-10-13. Pseudo-Anosovs are exponentially generic in mapping class groups. https://doi.org/10.2140/gt.2024.28.1923

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