  Anosov representations of word hyperbolic groups into higher-rank semisimple
Lie groups are representations with finite kernel and discrete image that have
strong analogies with convex cocompact representations into rank-one Lie
groups. However, the most naive analogy fails: generically, Anosov
representations do not act properly and cocompactly on a convex set in the
associated Riemannian symmetric space. We study representations into projective
indefinite orthogonal groups PO(p,q) by considering their action on the
associated pseudo-Riemannian hyperbolic space H^{p,q-1} in place of the
Riemannian symmetric space. Following work of Barbot and M\'erigot in anti-de
Sitter geometry, we find an intimate connection between Anosov representations
and the natural notion of convex cocompactness in this setting.
