Exotic mapping class group actions on the circle

Sang-hyun Kim; Thomas Koberda

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arXiv · 1603.02098

Exotic mapping class group actions on the circle

Sang-hyun Kim·Thomas Koberda

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Abstract

It has been known since the time of Nielsen that the mapping class group $\text{Mod}_{g,1}$ of a surface of genus $g$ and one puncture acts faithfully by homeomorphisms on the circle. In this note, we show that this standard representation of the mapping class group is not rigid, precisely, if $G<\text{Mod}_{g,1}$ is a finite index subgroup then there exist infinitely many non--conjugate faithful representations $G\to \text{Homeo}^+(S^1)$. We thus answer a question of B. Farb.

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BibTeX RIS

Sang-hyun Kim, Thomas Koberda. 2016-03-07. Exotic mapping class group actions on the circle. https://arxiv.org/abs/1603.02098

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