Reducible normal generators for mapping class groups are abundant
Geometric Topology
2023-10-10 v3 Dynamical Systems
Group Theory
Abstract
In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface normally generates the (pure) mapping class group of the subsurface. As an application, we provided a criterion for reducible mapping classes to normally generate the mapping class groups in terms of its asymptotic translation lengths on Teichm\"uller spaces. This is an analogue to the work of Lanier-Margalit dealing with pseudo-Anosov normal generators.
Cite
@article{arxiv.2112.13726,
title = {Reducible normal generators for mapping class groups are abundant},
author = {Hyungryul Baik and Dongryul M. Kim and Chenxi Wu},
journal= {arXiv preprint arXiv:2112.13726},
year = {2023}
}
Comments
11 pages, Final version, To appear in the Journal of Topology and Analysis