#### Volume 7, issue 4 (2007)

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Finite abelian subgroups of the mapping class group

### S Allen Broughton and Aaron Wootton

Algebraic & Geometric Topology 7 (2007) 1651–1697
 arXiv: math.AT/0611650
##### Abstract

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group ${\mathsc{ℳ}}_{\sigma }$ of a closed, smooth, orientable surface $S$ of genus $\sigma \ge 2$ is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumeration of finite abelian subgroups.

##### Keywords
finite subgroups of mapping class groups, automorphism groups of surfaces
##### Mathematical Subject Classification 2000
Primary: 20F34, 20F36, 14H37
Secondary: 14H30, 14J50