Anosov AdS representations are quasi-Fuchsian

  • Quentin Mérigot

    Université Joseph Fourier, Grenoble, France
  • Thierry Barbot

    Université d'Avignon, France


Let be a cocompact lattice in . A representation is called quasi-Fuchsian if it is faithful, discrete, and preserves an acausal subset in the boundary of anti-de Sitter space. A special case are Fuchsian representations, i.e., compositions of the inclusions and . We prove that quasi-Fuchsian representations are precisely those representations which are Anosov in the sense of Labourie (cf. (Lab06]). The study involves the geometry of locally anti-de Sitter spaces: quasi-Fuchsian representations are holonomy representations of globally hyperbolic spacetimes diffeomorphic to locally modeled on .

Cite this article

Quentin Mérigot, Thierry Barbot, Anosov AdS representations are quasi-Fuchsian. Groups Geom. Dyn. 6 (2012), no. 3, pp. 441–483

DOI 10.4171/GGD/163