Hitchin characters and geodesic laminations

Francis Bonahon; Guillaume Dreyer

doi:10.4310/acta.2017.v218.n2.a1

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arXiv · 1410.0729

Hitchin characters and geodesic laminations

Francis Bonahon·Guillaume Dreyer

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Abstract

For a closed surface S, the Hitchin component Hit_n(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group pi_1(S) to the Lie group PSL_n(R). We construct a parametrization of the Hitchin component that is well-adapted to a maximal geodesic lamination on the surface. This is a natural extension of Thurston's parametrization of the Teichmueller space of S by shear coordinates associated to a maximal geodesic lamination, corresponding to the case n=2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.

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BibTeX RIS

Francis Bonahon, Guillaume Dreyer. 2014-10-02. Hitchin characters and geodesic laminations. https://doi.org/10.4310/acta.2017.v218.n2.a1

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