Abelian Subgroups of the Torelli Group

William R. Vautaw

doi:10.2140/agt.2002.2.157

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Abelian Subgroups of the Torelli Group

William R. Vautaw

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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.

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William R. Vautaw. 2002-03-14. Abelian Subgroups of the Torelli Group. https://doi.org/10.2140/agt.2002.2.157

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