#### Vol. 302, No. 1, 2019

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A characterization of Fuchsian actions by topological rigidity

### Kathryn Mann and Maxime Wolff

Vol. 302 (2019), No. 1, 181–200
##### Abstract

We give a simple proof that any rigid representation of ${\pi }_{1}\left({\Sigma }_{g}\right)$ in ${Homeo}^{+}\left({S}_{1}\right)$ with Euler number at least $g$ is necessarily semiconjugate to a discrete, faithful representation into $PSL\left(2,ℝ\right)$. Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rigidity property. We have proved this result in greater generality, but with a much more involved proof, in arxiv:1710.04902.

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