Complex hyperbolic Kleinian groups with limit set a wild knot.
The authors construct explicitly a discrete representation \(\rho_{0}\) into \(PU(2,1)\) of a co-finite area Fuchsian group \(F< \text{PSL}(2,{\mathbb R})\) (which is a free group of finite rank) so that \(\rho_{0}(F)\) has a wild knot as limit set. In particular, they are able to see that the Teichmüller space of \(F\) (the \(PU(2,1)\) equivalence classes of all discrete representations of \(F\) into \(PU(2,1)\)) is not connected and that Toledo's invariant cannot identify different connected components of it.
scientific article; zbMATH DE number 2069741