#### 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
##### Publication
Received: 24 February 2012
Revised: 11 July 2012
Accepted: 22 December 2012
Published: 9 May 2013
##### Authors
 Hao Liang Department of Mathematics, Statistics, and Computer Science University of Illinois at Chicago 322 Science and Engineering Offices 851 S. Morgan Street Chicago, IL 60607-7045 USA http://homepages.math.uic.edu/~liang/