Algebraic & Geometric Topology

Finite abelian subgroups of the mapping class group

Allen Broughton and Aaron Wootton

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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 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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796770

Digital Object Identifier
doi:10.2140/agt.2007.7.1651

Mathematical Reviews number (MathSciNet)
MR2366175

Zentralblatt MATH identifier
1126.14038

Subjects
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

Keywords
finite subgroups of mapping class groups automorphism groups of surfaces

Citation

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. https://projecteuclid.org/euclid.agt/1513796770


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