Convex Foliated Projective Structures and the Hitchin Component for PSL(4,R)

Olivier Guichard (1) , Anna Wienhard (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 MATH-CHICAGO - Department of Mathematics

In this article we give a geometric interpretation of the Hitchin component for PSL(4,R) in the representation variety of a closed oriented surface of higher genus. We show that representations in the Hitchin component are precisely the holonomy representations of properly convex foliated projective structures on the unit tangent bundle of the surface. From this we also deduce a geometric description of the Hitchin component the symplectic group PSp(4,R).

Mots clés: Surface Groups; Hitchin Component; Projective Structures

Domaines: Géométrie différentielle [math.DG]

Olivier Guichard, Anna Wienhard. Convex Foliated Projective Structures and the Hitchin Component for PSL(4,R). 2007. ⟨hal-00129374v2⟩