English

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.

Keywords

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

R2 v1 2026-06-24T08:32:41.769Z