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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
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(2, ) 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