Abstract
We construct a geometric, real-analytic parameterization of the Hitchin component of the -character variety of a closed surface . 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 with finitely many leaves, we introduce two types of invariants for elements of the Hitchin component: shear invariants associated with each leaf of and triangle invariants associated with each component of the complement . We describe identities and relations satisfied by these invariants, and we use the resulting coordinates to parameterize the Hitchin component.
Citation
Francis Bonahon. Guillaume Dreyer. "Parameterizing Hitchin components." Duke Math. J. 163 (15) 2935 - 2975, 1 December 2014. https://doi.org/10.1215/0012794-2838654
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