Duke Mathematical Journal

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

Olivier Guichard and Anna Wienhard

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Abstract

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

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

Dates
First available in Project Euclid: 15 August 2008

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1218811400

Digital Object Identifier
doi:10.1215/00127094-2008-040

Mathematical Reviews number (MathSciNet)
MR2444302

Zentralblatt MATH identifier
1148.57027

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

Citation

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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