Finite abelian subgroups of the mapping class group

Broughton, Allen; Wootton, Aaron

doi:10.2140/agt.2007.7.1651

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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

DOI: 10.2140/agt.2007.7.1651

arXiv: math.AT/0611650

Abstract

The problem of enumeration of conjugacy classes of finite abelian subgroups of the mapping class group $ℳ_{σ}$ of a closed, smooth, orientable surface $S$ of genus $σ \geq 2$ 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

References

Publication

Received: 21 November 2006

Revised: 13 September 2007

Accepted: 13 September 2007

Published: 17 December 2007

Authors

S Allen Broughton
Department of Mathematics Rose Hulman Institute of Technology Terre Haute, IN 47803 USA
http://www.rose-hulman.edu/~brought/
Aaron Wootton
Department of Mathematics The University of Portland Portland, OR 97203 USA
http://faculty.up.edu/wootton/

Volume 7, issue 4 (2007)