The normal closure of a bounding pair map in its mapping class group
Geometric Topology
2025-10-15 v2 Group Theory
Abstract
Johnson showed that the normal subgroup of a mapping class group generated by the genus bounding pair maps is equal to the Torelli group. Generalizing Johnson's result, we give two descriptions of the normal subgroup generated by the genus bounding pair maps using the Chillingworth and the Casson--Morita invariants.
Keywords
Cite
@article{arxiv.2302.11673,
title = {The normal closure of a bounding pair map in its mapping class group},
author = {Lei Chen and Weiyan Chen and Justin Lanier},
journal= {arXiv preprint arXiv:2302.11673},
year = {2025}
}
Comments
v2: 20 pages, 9 figures. Version 1 contained an error in Proposition 4, and this invalidated the main result. Version 2 corrects this error and contains new main results. v1: 9 pages, 2 figures