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

preprint2016arXivOpen access

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.

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

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

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