Algebraic & Geometric Topology

Centralizers of finite subgroups of the mapping class group

Hao Liang

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In this paper, we study the action of finite subgroups of the mapping class group of a surface on the curve complex. We prove that if the diameter of the almost fixed point set of a finite subgroup H is big enough, then the centralizer of H is infinite.

Article information

Algebr. Geom. Topol., Volume 13, Number 3 (2013), 1513-1530.

Received: 24 February 2012
Revised: 11 July 2012
Accepted: 22 December 2012
First available in Project Euclid: 19 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups

finite subgroup of mapping class group curve complex hyperbolic group hierarchy


Liang, Hao. Centralizers of finite subgroups of the mapping class group. Algebr. Geom. Topol. 13 (2013), no. 3, 1513--1530. doi:10.2140/agt.2013.13.1513.

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