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arxiv: 1603.02098 · v3 · pith:XT2YNQ2Onew · submitted 2016-03-07 · 🧮 math.GT · math.GR

Exotic mapping class group actions on the circle

classification 🧮 math.GT math.GR
keywords classgroupmappingtextcircleactionsactsanswer
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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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