Pseudo-Anosovs are exponentially generic in mapping class groups
Geometric Topology
2024-07-24 v3 Group Theory
Abstract
Given a finite generating set , let us endow the mapping class group of a closed hyperbolic surface with the word metric for . We discuss the following question: does the proportion of non-pseudo-Anosov mapping classes in the ball of radius decrease to 0 as increases? We show that any finite subset of the mapping class group is contained in a finite generating set such that this proportion decreases exponentially. Our strategy applies to weakly hyperbolic groups and does not refer to the automatic structure of the group.
Keywords
Cite
@article{arxiv.2110.06678,
title = {Pseudo-Anosovs are exponentially generic in mapping class groups},
author = {Inhyeok Choi},
journal= {arXiv preprint arXiv:2110.06678},
year = {2024}
}
Comments
Expanded the introduction and elaborated several details. 33 pages and 6 figures. The final version of this paper will appear in Geometry and Topology