Abelian Subgroups of the Torelli Group
Geometric Topology
2014-10-01 v1 Group Theory
Abstract
Let S be a closed oriented surface of genus g > 1, and let T denote its Torelli group. First, given a set E of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on S, we determine precisely when a multitwist on E is an element of T by defining an equivalence relation on E and then applying graph theory. Second, we prove that an arbitrary Abelian subgroup of T has rank < 2g-4.
Cite
@article{arxiv.math/0203131,
title = {Abelian Subgroups of the Torelli Group},
author = {William R. Vautaw},
journal= {arXiv preprint arXiv:math/0203131},
year = {2014}
}
Comments
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-8.abs.html