Length functions of Hitchin representations

Dreyer, Guillaume¹

¹Department of Mathematics, University of Notre Dame, 255 Hurley Hall, Notre Dame, IN 46556, USA

Algebraic and Geometric Topology, Tome 13 (2013) no. 6, pp. 3153-3173

Résumé

Given a Hitchin representation ρ: π1(S) → PSLn(ℝ), we construct n continuous functions ℓiρ: C Höl(S) → ℝ defined on the space of Hölder geodesic currents C Höl(S) such that, for a closed, oriented curve γ in S, the i th eigenvalue of the matrix ρ(γ) ∈ PSLn(ℝ) is of the form ± expℓiρ(γ): such functions generalize to higher rank Thurston’s length function of Fuchsian representations. Identities and differentiability properties of these lengths ℓiρ, as well as applications to eigenvalue estimates, are also considered.

Détail

DOI : 10.2140/agt.2013.13.3153

Keywords: Hitchin representation, Anosov representation, length function, Hölder geodesic current

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