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

Wentworth, Richard¹ ; Wolf, Michael²

¹ Department of Mathematics, University of Maryland, College Park, MD 20742, United States
² Department of Mathematics, Rice University, MS 136, Houston, TX 77005-1892, United States

Geometry & topology, Tome 20 (2016) no. 5, pp. 3019-3032.

Résumé

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.

Détail

DOI : 10.2140/gt.2016.20.3019

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

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