https://hal-ens-lyon.archives-ouvertes.fr/ensl-00176526Barbot, ThierryThierryBarbotUMPA-ENSL - Unité de Mathématiques Pures et Appliquées - ENS Lyon - École normale supérieure - Lyon - CNRS - Centre National de la Recherche ScientifiqueQuasi-Fuchsian AdS representations are AnosovHAL CCSD2007Anti-de Sitter spacequasi-Fuchsian representationglobally hyperbolic spacetimeAnosov representation[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Barbot, Thierry2007-10-03 17:46:342022-02-07 10:48:022007-10-04 12:13:33enPreprints, Working Papers, ...https://hal-ens-lyon.archives-ouvertes.fr/ensl-00176526/documentapplication/pdf1In a recent paper, Q. Mérigot proved that representations in SO(2,n) of uniform lattices of SO(1,n) which are Anosov in the sense of Labourie are quasi-Fuchsian, i.e. are faithfull, discrete, and preserve an acausal subset in the boundary of anti-de Sitter space. In the present paper, we prove the reverse implication. It also includes: -- A construction of Dirichlet domains in the context of anti-de Sitter geometry, -- A proof that spatially compact globally hyperbolic anti-de Sitter spacetimes with acausal limit set admit locally CAT(-1) Cauchy hypersurfaces.