Abelian Subgroups of the Torelli Group

Details Abelian Subgroups of the Torelli Group Abelian Subgroups of the Torelli Group

2002-03-14

arxiv.org/abs/math/0203131v1

Algebr. Geom. Topol. 2 (2002) 157-170

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-8.abs.html

Scientific paper

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.

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