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

Abstract

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