Abelian subgroups of the Torelli group
Copyright policy )Abelian subgroups of the Torelli group
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.
Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol2/agt-2-8.abs.html
- Michigan State University United States
General low-dimensional topology, 20F38, 57M60, 20F38, Dehn twists, Geometric Topology (math.GT), mapping class group, Group Theory (math.GR), mapping class groups, Torelli group, 57M60, Mathematics - Geometric Topology, multitwist, FOS: Mathematics, Group actions on manifolds and cell complexes in low dimensions, Torelli groups, Mathematics - Group Theory, Other groups related to topology or analysis
General low-dimensional topology, 20F38, 57M60, 20F38, Dehn twists, Geometric Topology (math.GT), mapping class group, Group Theory (math.GR), mapping class groups, Torelli group, 57M60, Mathematics - Geometric Topology, multitwist, FOS: Mathematics, Group actions on manifolds and cell complexes in low dimensions, Torelli groups, Mathematics - Group Theory, Other groups related to topology or analysis
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