Finite Abelian Subgroups of the Mapping Class Group

Abstract

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $\mathcal{M}_σ$ of a compact closed surface $X$ of genus $σ$ is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumeration of finite abelian subgroups.