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June 2017 Hitchin characters and geodesic laminations
Francis Bonahon, Guillaume Dreyer
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Acta Math. 218(2): 201-295 (June 2017). DOI: 10.4310/ACTA.2017.v218.n2.a1


For a closed surface $S$, the Hitchin component $\mathrm{Hit}_n (S)$ is a preferred component of the character variety consisting of group homomorphisms from the fundamental group $\pi_1(S)$ to the Lie group $\mathrm{PSL}_n (\mathbb{R})$. We construct a parametrization of the Hitchin component that is well-adapted to a geodesic lamination $\lambda$ on the surface. This is a natural extension of Thurston’s parametrization of the Teichmüller space $\mathcal{T}(S)$ by shearing coordinates associated with $\lambda$, corresponding to the case $n=2$. However, significantly new ideas are needed in this higher-dimensional case. The article concludes with a few applications.

Funding Statement

This research was partially supported by the grants DMS-0604866, DMS-1105402 and DMS-1406559 from the U.S. National Science Foundation, and by a Fellowship from the Simons Foundation (grant 301050). In addition, the authors gratefully acknowledge support from the NSF grants DMS-1107452, 1107263 and 1107367 “RNMS: GEometric structures And Representation varieties” (the GEAR Network).


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Francis Bonahon. Guillaume Dreyer. "Hitchin characters and geodesic laminations." Acta Math. 218 (2) 201 - 295, June 2017.


Received: 26 May 2015; Revised: 19 March 2017; Published: June 2017
First available in Project Euclid: 31 January 2018

zbMATH: 06826206
MathSciNet: MR3733100
Digital Object Identifier: 10.4310/ACTA.2017.v218.n2.a1

Rights: Copyright © 2017 Institut Mittag-Leffler


Vol.218 • No. 2 • June 2017
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