Finite Abelian Subgroups of the Mapping Class Group
The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group ℳσ of a closed, smooth, orientable surface S of genus σ ≥ 2 is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumeration of finite abelian subgroups.
Broughton, Sean A. and Wootton, Aaron, "Finite Abelian Subgroups of the Mapping Class Group" (2007). Faculty Publications - Mathematics. 6.