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

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

2007-02-07

arxiv.org/abs/math/0702184v2

Mathematics

Differential Geometry

Scientific paper

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).

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