Complex hyperbolic Kleinian groups with limit set a wild knot

AbstractWe construct quasi-Fuchsian groups acting on two-dimensional complex hyperbolic space with limit set a wild knot. Also, we study the Teichmüller space T(G) of faithful, discrete, type-preserving representations of a Fuchsian group G of the first kind with parabolic elements in complex hyperbolic space. We show that T(G) is not connected, and that the Toledo invariant does not distinguish different connected components of T(G)