## Algebraic & Geometric Topology

### Abelian subgroups of the Torelli group

William R Vautaw

#### Abstract

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 $≤2g−3$.

#### Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 157-170.

Dates
Revised: 24 February 2002
Accepted: 28 February 2002
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.agt/1513882688

Digital Object Identifier
doi:10.2140/agt.2002.2.157

Mathematical Reviews number (MathSciNet)
MR1917048

Zentralblatt MATH identifier
0997.57035

Subjects
Primary: 57M60: Group actions in low dimensions
Secondary: 20F38: Other groups related to topology or analysis

#### Citation

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

#### References

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