Mathematics > Differential Geometry
[Submitted on 4 Oct 2007]
Title:Quasi-Fuchsian AdS representations are Anosov
View PDFAbstract: In 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.
Submission history
From: Thierry Barbot [view email] [via CCSD proxy][v1] Thu, 4 Oct 2007 10:13:24 UTC (26 KB)
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