Quasi-Fuchsian AdS representations are AnosovReport as inadecuate

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1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

Abstract : In a recent paper, Q.
Mérigot proved that representations in SO2,n of uniform lattices of SO1,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.

keyword : Anti-de Sitter space quasi-Fuchsian representation globally hyperbolic spacetime Anosov representation

Author: Thierry Barbot -

Source: https://hal.archives-ouvertes.fr/


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