Virtual critical regularity of mapping class group actions on the circle

Sang-hyun Kim; Thomas Koberda; Cristóbal Rivas

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arXiv · 2104.15073

Virtual critical regularity of mapping class group actions on the circle

Sang-hyun Kim·Thomas Koberda·Cristóbal Rivas

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Abstract

We show that if $G_1$ and $G_2$ are non-solvable groups, then no $C^{1,\tau}$ action of $(G_1\times G_2)*\mathbb{Z}$ on $S^1$ is faithful for $\tau>0$. As a corollary, if $S$ is an orientable surface of complexity at least three then the critical regularity of an arbitrary finite index subgroup of the mapping class group $\mathrm{Mod}(S)$ with respect to the circle is at most one, thus strengthening a result of the first two authors with Baik.

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BibTeX RIS

Sang-hyun Kim, Thomas Koberda, Cristóbal Rivas. 2021-04-30. Virtual critical regularity of mapping class group actions on the circle. https://arxiv.org/abs/2104.15073

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