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 $H^4$, and the other by a rotation of order 21 and a reflection of $H^6$. For each of them, we also locate convex cocompact subgroups with limit set a Menger curve.