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

 Recent Issues Vol. 305: 1  2 Vol. 304: 1  2 Vol. 303: 1  2 Vol. 302: 1  2 Vol. 301: 1  2 Vol. 300: 1  2 Vol. 299: 1  2 Vol. 298: 1  2 Online Archive Volume: Issue:
 The Journal Editorial Board Subscriptions Officers Special Issues Submission Guidelines Submission Form Contacts ISSN: 1945-5844 (e-only) ISSN: 0030-8730 (print) Author Index To Appear Other MSP Journals
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.

##### Keywords
rigidity, geometricity, Euler class, surface group actions on the circle
##### Mathematical Subject Classification 2010
Primary: 20H10, 37E10, 37E45, 57S25, 58D29