Algebraic & Geometric Topology

Length functions of Hitchin representations

Guillaume Dreyer

Abstract

Given a Hitchin representation $ρ:π1(S)→ PSLn(ℝ)$, we construct $n$ continuous functions defined on the space of Hölder geodesic currents such that, for a closed, oriented curve $γ$ in $S$, the 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.

Article information

Source
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3153-3173.

Dates
Revised: 4 February 2013
Accepted: 19 March 2013
First available in Project Euclid: 19 December 2017

https://projecteuclid.org/euclid.agt/1513715728

Digital Object Identifier
doi:10.2140/agt.2013.13.3153

Mathematical Reviews number (MathSciNet)
MR3248729

Zentralblatt MATH identifier
1285.57010

Citation

Dreyer, Guillaume. Length functions of Hitchin representations. Algebr. Geom. Topol. 13 (2013), no. 6, 3153--3173. doi:10.2140/agt.2013.13.3153. https://projecteuclid.org/euclid.agt/1513715728

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