Convex Foliated Projective Structures and the Hitchin Component for PSL(4,R) - Archive ouverte HAL Access content directly
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Convex Foliated Projective Structures and the Hitchin Component for PSL(4,R)

Olivier Guichard
Anna Wienhard
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Abstract

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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Dates and versions

hal-00129374 , version 1 (07-02-2007)
hal-00129374 , version 2 (05-06-2007)

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