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2002 Abelian subgroups of the Torelli group
William R Vautaw
Algebr. Geom. Topol. 2(1): 157-170 (2002). DOI: 10.2140/agt.2002.2.157

Abstract

Let S be a closed oriented surface of genus g2, 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 2g3.

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William R Vautaw. "Abelian subgroups of the Torelli group." Algebr. Geom. Topol. 2 (1) 157 - 170, 2002. https://doi.org/10.2140/agt.2002.2.157

Information

Received: 12 December 2001; Revised: 24 February 2002; Accepted: 28 February 2002; Published: 2002
First available in Project Euclid: 21 December 2017

zbMATH: 0997.57035
MathSciNet: MR1917048
Digital Object Identifier: 10.2140/agt.2002.2.157

Subjects:
Primary: 57M60
Secondary: 20F38

Rights: Copyright © 2002 Mathematical Sciences Publishers

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