A characterization of Fuchsian actions by topological rigidity

Abstract

We prove that any rigid representation of π1Σg in Homeo + (S 1 ) with Euler number at least g is necessarily semi-conjugate 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. Though independent, this work can be read as an introduction to the companion paper [10] by the same authors.