Topological proof of Benoist-Quint's orbit closure theorem for SO(d,1)

Abstract

We present a new proof of the following theorem of Benoist-Quint: Let $G:=S{O}^{\circ }(d,1)$, $d\ge 2$ and $\Delta <G$ a cocompact lattice. Any orbit of a Zariski dense subgroup $\Gamma$ of $G$ is either finite or dense in $\Delta \backslash G$. While Benoist and Quint's proof is based on the classification of stationary measures, our proof is topological, using ideas from the study of dynamics of unipotent flows on the infinite volume homogeneous space $\Gamma \backslash G$.

14 pages (new title), to appear in JMD

References in corpus (1)

• Orbit closures of unipotent flows for hyperbolic manifolds with Fuchsian ends

Cited by in corpus (1)

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