Hitchin characters and geodesic laminations

Abstract

For a closed surface S, the Hitchin component 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 PSL_n(R). We construct a parametrization of the Hitchin component that is well-adapted to a maximal geodesic lamination on the surface. This is a natural extension of Thurston's parametrization of the Teichmueller space of S by shear coordinates associated to a maximal geodesic lamination, corresponding to the case n=2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.

67 pages, 9 figures. Version 2: Minor polish (misprints, etc.) prior to submission

Cited by in corpus (4)

• Shear-shape cocycles for measured laminations and ergodic theory of the earthquake flow
• A dynamical perspective on shear-bend coordinates
• Cataclysms for Anosov representations
• Shearing deformations of Hitchin representations and the Atiyah-Bott-Goldman symplectic form