Let Γ be a cocompact lattice in SO(1,n). A representation ρ:Γ→SO(2,n) is called quasi-Fuchsian if it is faithful, discrete, and preserves an acausal subset in the boundary of anti-de Sitter space. A special case are Fuchsian representations, i.e., compositions of the inclusions Γ⊂SO(1,n) and SO(1,n)⊂SO(2,n). We prove that quasi-Fuchsian representations are precisely those representations which are Anosov in the sense of Labourie (cf. (Lab06]). The study involves the geometry of locally anti-de Sitter spaces: quasi-Fuchsian representations are holonomy representations of globally hyperbolic spacetimes diffeomorphic to R×Γ\Hn locally modeled on AdSn+1.
@article{10_4171_ggd_163,
author = {Thierry Barbot and Quentin M\'erigot},
title = {Anosov {AdS} representations are {quasi-Fuchsian}},
journal = {Groups, geometry, and dynamics},
pages = {441--483},
year = {2012},
volume = {6},
number = {3},
doi = {10.4171/ggd/163},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/163/}
}
TY - JOUR
AU - Thierry Barbot
AU - Quentin Mérigot
TI - Anosov AdS representations are quasi-Fuchsian
JO - Groups, geometry, and dynamics
PY - 2012
SP - 441
EP - 483
VL - 6
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/163/
DO - 10.4171/ggd/163
ID - 10_4171_ggd_163
ER -
