1 December 2014 Parameterizing Hitchin components
Francis Bonahon, Guillaume Dreyer
Duke Math. J. 163(15): 2935-2975 (1 December 2014). DOI: 10.1215/0012794-2838654


We construct a geometric, real-analytic parameterization of the Hitchin component Hitn(S) of the PSLn(R)-character variety RPSLn(R)(S) of a closed surface S. The approach is explicit and constructive. In essence, our parameterization is an extension of Thurston’s shearing coordinates for the Teichmüller space of a closed surface, combined with Fock–Goncharov’s coordinates for the moduli space of positive framed local systems of a punctured surface. More precisely, given a maximal geodesic lamination λS with finitely many leaves, we introduce two types of invariants for elements of the Hitchin component: shear invariants associated with each leaf of λ and triangle invariants associated with each component of the complement Sλ. We describe identities and relations satisfied by these invariants, and we use the resulting coordinates to parameterize the Hitchin component.


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Francis Bonahon. Guillaume Dreyer. "Parameterizing Hitchin components." Duke Math. J. 163 (15) 2935 - 2975, 1 December 2014. https://doi.org/10.1215/0012794-2838654


Published: 1 December 2014
First available in Project Euclid: 1 December 2014

zbMATH: 1326.32023
MathSciNet: MR3285861
Digital Object Identifier: 10.1215/0012794-2838654

Primary: 58D57
Secondary: 20H10

Keywords: Anosov representation , geodesic lamination , Hitchin component , Hitchin representation , positive representation , shear invariant

Rights: Copyright © 2014 Duke University Press


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Vol.163 • No. 15 • 1 December 2014
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