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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Abelian subgroups of the Torelli group

William R Vautaw

Algebraic & Geometric Topology 2 (2002) 157–170

arXiv: math.GT/0203131

Abstract

Let S be a closed oriented surface of genus g 2, 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 3.

Keywords
mapping class group, Torelli group, multitwist
Mathematical Subject Classification 2000
Primary: 57M60
Secondary: 20F38
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Publication
Received: 12 December 2001
Revised: 24 February 2002
Accepted: 28 February 2002
Published: 6 March 2002
Authors
William R Vautaw
Department of Mathematics
Michigan State University
East Lansing MI 48824
USA