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

Wentworth, Richard; Wolf, Michael

doi:10.2140/gt.2016.20.3019

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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

DOI: 10.2140/gt.2016.20.3019

Abstract

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

Keywords

spectral curve, Higgs bundle, complex projective structure, R-tree

Mathematical Subject Classification 2010

Primary: 30F60, 32G15, 53C07, 70S15

Secondary: 30F40, 53C43

References

Publication

Received: 3 August 2015

Accepted: 2 January 2016

Published: 7 October 2016

Proposed: Benson Farb

Seconded: Bruce Kleiner, John Lott

Authors

Richard A Wentworth
Department of Mathematics University of Maryland College Park, MD 20742 United States

Michael Wolf
Department of Mathematics Rice University MS 136 Houston, TX 77005-1892 United States

Volume 20, issue 5 (2016)