Surface group representations to $SL(2,{\mathbb C})$ and Higgs bundles with smooth spectral data

Abstract

We show that for every nonelementary representation of a surface group into $SL(2,{\mathbb C})$ there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the discriminant locus of the Hitchin fibration.

15 pages. Revised version. To appear in Geometry and Topology