A positive proportion of elements of mapping class groups is pseudo-Anosov
Group Theory
2018-04-04 v2 Geometric Topology
Abstract
In the Cayley graph of the mapping class group of a closed surface, with respect to any generating set, we look at a ball of large radius centered on the identity vertex, and at the proportion among the vertices in this ball representing pseudo-Anosov elements. A well-known conjecture states that this proportion should tend to one as the radius tends to infinity. We prove that it stays bounded away from zero. We also prove similar results for a large class of subgroups of the mapping class group.
Cite
@article{arxiv.1703.05044,
title = {A positive proportion of elements of mapping class groups is pseudo-Anosov},
author = {María Cumplido and Bert Wiest},
journal= {arXiv preprint arXiv:1703.05044},
year = {2018}
}
Comments
6 pages