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arxiv: math/0401230 · v2 · submitted 2004-01-19 · 🧮 math.DG

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Anosov Flows, Surface Groups and Curves in Projective Space

Francois Labourie
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classification 🧮 math.DG
keywords projectivespacecomponentrepresentationssurfaceanosovcurvesflows
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In 1990, Hitchin's proved a component of the space of representations of a surface group in SL(n,R) is homeomorphic to a ball. For n=2,3 this component has been identified with the holonomies of geometric structures (hyperbolic for n=2, or real projective for n=3). In the preprint "Anosov flows, Surface groups and Curves in Projective Space", we extend this interpretation to higher dimension and show every representation in Hitchin's component is attached to a (special) curve in projective space, thus giving a geometric interpretation of these representations. We also prove these representations are faithful, discrete and purely loxodromic (or hyperbolic)

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. On separated families of Anosov representations

    math.GT 2026-04 unverdicted novelty 7.0

    Separated families of Anosov representations have critical exponents asymptotic to a combinatorial invariant computable from finite graph spectral data, yielding bounds on the Thurston asymmetric metric and analysis o...

  2. On separated families of Anosov representations

    math.GT 2026-04 unverdicted novelty 5.0

    For separated families of Anosov representations, the critical exponent along diverging sequences asymptotes to a combinatorial invariant from the spectral data of a finite graph.