Dynamics for discrete subgroups of ${\mathrm{SL}}_2(\mathbb{C})$

Abstract

Margulis wrote in the preface of his book Discrete subgroups of semisimple Lie groups that "A number of important topics have been omitted. The most significant of these is the theory of Kleinian groups and Thurston's theory of 3-dimensional manifolds: these two theories can be united under the common title of Theory of discrete subgroups of ${\mathrm{SL}}_2(\mathbb{C})$." In this article, we will discuss a few recent advances regarding this missing topic from his book, which were influenced by his earlier works.

The statement of Lemma 5.1(1) corrected

References in corpus (3)

• Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends
• Arithmeticity of hyperbolic 3-manifolds containing infinitely many totally geodesic surfaces
• Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1)