4/30/2009

Thierry Barbot
Universite d'Avignon

Quasi-Fuchsian representations into SO(2,n)

Let Gamma be a uniform lattice in SO(1,n). We consider representations rho: Gamma into R (the reals) which can be continuously deformed to a Fuchsian representation, i.e. a representation induced by the inclusions Gamma subset SO(1,n) subset SO(2,n). We prove that all these representations are faithfull and discrete. They are actually quasi-Fuchsian, a property involving the geometry of anti-de Sitter space (lorentzian analog of the hyperbolic space) which will be described.