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Length functions of Hitchin representations

Guillaume Dreyer

Algebraic & Geometric Topology 13 (2013) 3153–3173
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.

Keywords
Hitchin representation, Anosov representation, length function, Hölder geodesic current
Mathematical Subject Classification
Primary: 57M50
Secondary: 57M05, 37F30, 22E40
References
Publication
Received: 11 September 2012
Revised: 4 February 2013
Accepted: 19 March 2013
Published: 11 September 2013
Authors
Guillaume Dreyer
Department of Mathematics
University of Notre Dame
255 Hurley Hall
Notre Dame, IN 46556
USA