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

Sami Douba; Gye-Seon Lee; Ludovic Marquis; Lorenzo Ruffoni

doi:10.1112/blms.70319

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arXiv · 2502.09470

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

Sami Douba·Gye-Seon Lee·Ludovic Marquis·Lorenzo Ruffoni

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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.

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Sami Douba, Gye-Seon Lee, Ludovic Marquis, Lorenzo Ruffoni. 2025-02-13. Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere. https://doi.org/10.1112/blms.70319

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