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Exotic Mapping Class Group Actions on the Circle by Kim, Sang-hyun; Koberda, Thomas is a scholarly article available to read on EtoBox.

What is Exotic Mapping Class Group Actions on the Circle about?

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.

Author

Kim, Sang-hyun; Koberda, Thomas

Published

2016

Language

EN