Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 2, Number 1 (2002), 157-170.
Abelian subgroups of the Torelli group
Let be a closed oriented surface of genus , and let denote its Torelli group. First, given a set of homotopically nontrivial, pairwise disjoint, pairwise nonisotopic simple closed curves on , we determine precisely when a multitwist on is an element of by defining an equivalence relation on and then applying graph theory. Second, we prove that an arbitrary Abelian subgroup of has rank .
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 157-170.
Received: 12 December 2001
Revised: 24 February 2002
Accepted: 28 February 2002
First available in Project Euclid: 21 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M60: Group actions in low dimensions
Secondary: 20F38: Other groups related to topology or analysis
Vautaw, William R. Abelian subgroups of the Torelli group. Algebr. Geom. Topol. 2 (2002), no. 1, 157--170. doi:10.2140/agt.2002.2.157. https://projecteuclid.org/euclid.agt/1513882688