Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere

Abstract

We exhibit two examples of convex cocompact subgroups of the isometry groups of real hyperbolic spaces with limit set a Pontryagin sphere: one generated by $50$ reflections of ${\mathbb{H}}^4$, and the other by a rotation of order $21$ and a reflection of ${\mathbb{H}}^6$. For each of them, we also locate convex cocompact subgroups with limit set a Menger curve.

15 pages, 5 figures. Accepted for publication in Bulletin of the London Mathematical Society