Algebraic & Geometric Topology

Finite abelian subgroups of the mapping class group

Allen Broughton and Aaron Wootton

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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 σ2 is considered. A complete method of enumeration is achieved for finite elementary abelian subgroups and steps are taken toward enumeration of finite abelian subgroups.

Article information

Algebr. Geom. Topol., Volume 7, Number 4 (2007), 1651-1697.

Received: 21 November 2006
Revised: 13 September 2007
Accepted: 13 September 2007
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F34: Fundamental groups and their automorphisms [See also 57M05, 57Sxx] 20F36: Braid groups; Artin groups 14H37: Automorphisms
Secondary: 14H30: Coverings, fundamental group [See also 14E20, 14F35] 14J50: Automorphisms of surfaces and higher-dimensional varieties

finite subgroups of mapping class groups automorphism groups of surfaces


Broughton, Allen; Wootton, Aaron. Finite abelian subgroups of the mapping class group. Algebr. Geom. Topol. 7 (2007), no. 4, 1651--1697. doi:10.2140/agt.2007.7.1651.

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