Quasi-Fuchsian AdS representations are Anosov
Differential Geometry
2007-10-05 v1
Abstract
In a recent paper, Q. M\'erigot 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.
Keywords
Cite
@article{arxiv.0710.0969,
title = {Quasi-Fuchsian AdS representations are Anosov},
author = {Thierry Barbot},
journal= {arXiv preprint arXiv:0710.0969},
year = {2007}
}