Algebraic & Geometric Topology

Length functions of Hitchin representations

Guillaume Dreyer

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Abstract

Given a Hitchin representation ρ:π1(S) PSLn(), we construct n continuous functions iρ:C Höl(S) 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() is of the form ± expiρ(γ): such functions generalize to higher rank Thurston’s length function of Fuchsian representations. Identities and differentiability properties of these lengths iρ, as well as applications to eigenvalue estimates, are also considered.

Article information

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

Dates
Received: 11 September 2012
Revised: 4 February 2013
Accepted: 19 March 2013
First available in Project Euclid: 19 December 2017

Permanent link to this document
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

Keywords
Hitchin representation Anosov representation length function Hölder geodesic current

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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