#### Volume 13, issue 3 (2013)

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Centralizers of finite subgroups of the mapping class group

### Hao Liang

Algebraic & Geometric Topology 13 (2013) 1513–1530
##### Abstract

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.

##### Keywords
finite subgroup of mapping class group, curve complex, hyperbolic group, hierarchy
##### Mathematical Subject Classification 2010
Primary: 20F65, 20F67