Algebraic & Geometric Topology
- Algebr. Geom. Topol.
- Volume 13, Number 6 (2013), 3153-3173.
Length functions of Hitchin representations
Given a Hitchin representation , we construct continuous functions defined on the space of Hölder geodesic currents such that, for a closed, oriented curve in , the eigenvalue of the matrix is of the form : such functions generalize to higher rank Thurston’s length function of Fuchsian representations. Identities and differentiability properties of these lengths , as well as applications to eigenvalue estimates, are also considered.
Algebr. Geom. Topol., Volume 13, Number 6 (2013), 3153-3173.
Received: 11 September 2012
Revised: 4 February 2013
Accepted: 19 March 2013
First available in Project Euclid: 19 December 2017
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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