Centralizers of Finite Subgroups of the Mapping Class Group
Hao Liang
TL;DR
This paper investigates how finite subgroups of the mapping class group act on the curve complex, showing that large fixed point sets imply infinite centralizers, thus revealing structural properties of these groups.
Contribution
It establishes a new link between the size of fixed point sets and the infinitude of centralizers in the mapping class group.
Findings
Large fixed point sets imply infinite centralizers.
Finite subgroup actions are closely related to the geometry of the curve complex.
Provides new insights into the structure of the mapping class group.
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.
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