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 .
"Abelian subgroups of the Torelli group." Algebr. Geom. Topol. 2 (1) 157 - 170, 2002. https://doi.org/10.2140/agt.2002.2.157