A characterization of Fuchsian actions by topological rigidity

Kathryn Mann; Maxime Wolff

doi:10.2140/pjm.2019.302.181

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arXiv · 1711.05665

A characterization of Fuchsian actions by topological rigidity

Kathryn Mann·Maxime Wolff

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Abstract

We prove that any rigid representation of $\pi_1\Sigma_g$ in $\mathrm{Homeo}_+(S^1)$ with Euler number at least $g$ is necessarily semi-conjugate to a discrete, faithful representation into $\mathrm{PSL}(2,\mathbb{R})$. Combined with earlier work of Matsumoto, this precisely characterizes Fuchsian actions by a topological rigidity property. Though independent, this work can be read as an introduction to the companion paper {\em rigidity and geometricity for surface group actions on the circle}, by the same authors.

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Kathryn Mann, Maxime Wolff. 2017-11-15. A characterization of Fuchsian actions by topological rigidity. https://doi.org/10.2140/pjm.2019.302.181

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