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 π1(Σg) in Homeo+(S1) with Euler number at least g is necessarily semiconjugate to a discrete, faithful representation into PSL(2, ). 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