Volume 7, issue 4 (2007)

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ISSN (electronic): 1472-2739
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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 σ 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 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/