Duke Mathematical Journal
- Duke Math. J.
- Volume 163, Number 15 (2014), 2935-2975.
Parameterizing Hitchin components
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.
Duke Math. J., Volume 163, Number 15 (2014), 2935-2975.
First available in Project Euclid: 1 December 2014
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Secondary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]
Bonahon, Francis; Dreyer, Guillaume. Parameterizing Hitchin components. Duke Math. J. 163 (2014), no. 15, 2935--2975. doi:10.1215/0012794-2838654. https://projecteuclid.org/euclid.dmj/1417442576