Discrete subgroups of $\rm{PSL}_2(\mathbb C)$ are called Kleinian groups. Mostow rigidity theorem (1968) says that Kleinian groups of finite co-volume (=lattices) do not admit any faithful discrete representation into $\rm{PSL}_2(\mathbb C)$ except for conjugations. I will present a new rigidity theorem for finitely generated Kleinian groups which are not necessarily lattices, and explain how this theorem compares with Sullivan’s rigidity theorem (1981).
This talk is based on joint work with Dongryul Kim.