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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747

Finite abelian subgroups of the mapping class group

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 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.

Keywords

finite subgroups of mapping class groups, automorphism groups of surfaces

Mathematical Subject Classification

Primary: 14H37, 20F34, 20F36

Secondary: 14H30, 14J50

References
Publication

Received: 21 November 2006
Revised: 13 September 2007
Accepted: 13 September 2007
Published: 17 December 2007

Authors
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/