HITCHIN CHARACTERS AND GEODESIC LAMINATIONS

For a closed surface S, the Hitchin component Hitn(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group �1(S) to the Lie group PSLn(R). We construct a parametrization of the Hitchin component that is well-adapted to a geodesic laminationon the surface. This is a natural extension of Thurston's parametrization of the Teichmuller space T(S) by shear coordinates associated to �, corresponding to the case n = 2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.