Geodesic
Abelian subgroups of the Torelli group
Vautaw, William R1
1Department of Mathematics, Michigan State University, East Lansing MI 48824, USA
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 157-170
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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.

DOI : 10.2140/agt.2002.2.157
Keywords: mapping class group, Torelli group, multitwist

Vautaw, William R  1

1 Department of Mathematics, Michigan State University, East Lansing MI 48824, USA 
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Vautaw, William R. Abelian subgroups of the Torelli group. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 157-170. doi: 10.2140/agt.2002.2.157

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