Generating the Torelli group
Geometric Topology
2012-02-29 v2 Group Theory
Abstract
We give a new proof of the theorem of Birman-Powell that the Torelli subgroup of the mapping class group of a closed orientable surface of genus at least 3 is generated by simple homeomorphisms known as bounding pair maps. The key ingredient is a proof that the subcomplex of the curve complex of the surface spanned by curves within a fixed homology class is connected.
Cite
@article{arxiv.1110.0876,
title = {Generating the Torelli group},
author = {Allen Hatcher and Dan Margalit},
journal= {arXiv preprint arXiv:1110.0876},
year = {2012}
}
Comments
23 pages, 10 figures, improvements to the exposition, to appear in L'Enseignement Mathematique