  We construct convex-cocompact representations of fundamental groups of closed
hyperbolic surfaces into the isometry group of the infinite-dimensional
hyperbolic space using bendings. We prove that convex-cocompact representations
of finitely generated groups in the group of isometries of the
infinite-dimensional hyperbolic space form an open set in the space of
representations and that the space of deformations (up to conjugation) obtained
by bending an irreducible representation of a surface group is
infinite-dimensional.
