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

By Olivier Y Guichard, Anna Wienhard. 2007

51 citations recorded by the source corpus.

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).

View Paper: https://www.semanticscholar.org/paper/0d15faf56fb818279b785439b86f0e043429640e

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Citations in the corpus

Locally Homogeneous Geometric Manifolds (2010, background): “Many diverse examples of RP3-structures on twisted S1-bundles over closed hyperbolic surfaces arise from maximal representations of surface groups into Sp(4,R) by Guichard-Wienhard [101].”
AN INVITATION TO HIGHER TEICHMÜLLER THEORY (2019, methodology): “Hitchin [2016], or algebraic structures developed in Labourie [2017b] and Sun [2017a,b].”
Topological invariants of Anosov representations (2009, background): “and the set of geodesic leaves is parametrized by @ 1() (2) = @ 1() 2 , the complementary of the diagonal in @ 1() 2. (For more details we refer the reader to [ 21, Section 1.1 ].)”