David Xu

Convex cocompact representations of groups into PSL(2,R) have been widely studied as a generalisation of the theory of Fuchsian representations. A further natural generalisation of this theory is to consider representations into the isometry groups of higher dimensional hyperbolic spaces, PO(n,1). If G is a finitely generated group, it is well known that a convex cocompact representation of G into PO(n,1) has an open neighbourhood consisting of convex cocompact representations. We may wonder if this is still true for representations into the isometry group of the infinite dimensional hyperbolic space.