A characterization of Fuchsian actions by topological rigidity

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.

Companion paper to arXiv:1710.04902 [math.GT] by the same authors. This article gives a simple proof of a special case

Cited by in corpus (2)

• Rigidity of mapping class group actions on $S^1$
• Rigidity and geometricity for surface group actions on the circle