#### Volume 20, issue 5 (2016)

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

### Richard A Wentworth and Michael Wolf

Geometry & Topology 20 (2016) 3019–3032
##### 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.

##### Keywords
spectral curve, Higgs bundle, complex projective structure, R-tree
##### Mathematical Subject Classification 2010
Primary: 30F60, 32G15, 53C07, 70S15
Secondary: 30F40, 53C43