Duke Mathematical Journal

Convex foliated projective structures and the Hitchin component for PSL4(R)

Olivier Guichard and Anna Wienhard

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In this article, we give a geometric interpretation of the Hitchin component T4(Σ)Rep(π1(Σ),PSL4(R)) of a closed oriented surface of genus g2. We show that representations in T4(Σ) are precisely the holonomy representations of properly convex foliated projective structures on the unit tangent bundle of Σ. From this, we also deduce a geometric description of the Hitchin component T(Σ,Sp4(R)) of representations into the symplectic group

Article information

Duke Math. J., Volume 144, Number 3 (2008), 381-445.

First available in Project Euclid: 15 August 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M50: Geometric structures on low-dimensional manifolds
Secondary: 20H10: Fuchsian groups and their generalizations [See also 11F06, 22E40, 30F35, 32Nxx]


Guichard, Olivier; Wienhard, Anna. Convex foliated projective structures and the Hitchin component for ${\rm PSL}_4(\mathbf{R})$. Duke Math. J. 144 (2008), no. 3, 381--445. doi:10.1215/00127094-2008-040. https://projecteuclid.org/euclid.dmj/1218811400

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