A characterization of Fuchsian actions by topological rigidity

We give a simple proof that any rigid representation of $π_{1} (Σ_{g})$ in ${Homeo}^{+} (S_{1})$ with Euler number at least $g$ is necessarily semiconjugate to a discrete, faithful representation into $PSL (2, ℝ)$ . 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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Keywords

rigidity, geometricity, Euler class, surface group actions on the circle

Mathematical Subject Classification 2010

Primary: 20H10, 37E10, 37E45, 57S25, 58D29

Milestones

Received: 9 March 2018

Revised: 16 January 2019

Accepted: 21 January 2019

Published: 5 November 2019

Authors

Kathryn Mann
Department of Mathematics Cornell University Ithaca, NY United States

Maxime Wolff
Sorbonne Université Université Paris Diderot CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG Paris France

Vol. 302, No. 1, 2019

Kathryn Mann and Maxime Wolff

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors