An infinite presentation of the Torelli group
Abstract
In this paper, we construct an infinite presentation of the Torelli subgroup of the mapping class group of a surface whose generators consist of the set of all "separating twists", all "bounding pair maps", and all "commutators of simply intersecting pairs" and whose relations all come from a short list of topological configurations of these generators on the surface. Aside from a few obvious ones, all of these relations come from a set of embeddings of groups derived from surface groups into the Torelli group. In the process of analyzing these embeddings, we derive a novel presentation for the fundamental group of a closed surface whose generating set is the set of all simple closed curves.
Cite
@article{arxiv.math/0703529,
title = {An infinite presentation of the Torelli group},
author = {Andrew Putman},
journal= {arXiv preprint arXiv:math/0703529},
year = {2020}
}
Comments
52 pages, 14 figures, 1 table, very heavily revised and expanded, section on obtaining presentations from group actions spun off as separate paper; to appear in GAFA