Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866912996812390400 |
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| author | Douba, Sami Lee, Gye-Seon Marquis, Ludovic Ruffoni, Lorenzo |
| author_facet | Douba, Sami Lee, Gye-Seon Marquis, Ludovic Ruffoni, Lorenzo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09470 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere Douba, Sami Lee, Gye-Seon Marquis, Ludovic Ruffoni, Lorenzo Geometric Topology Group Theory 20F65, 20F67, 22E40, 20F55 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. |
| title | Convex cocompact groups in real hyperbolic spaces with limit set a Pontryagin sphere |
| topic | Geometric Topology Group Theory 20F65, 20F67, 22E40, 20F55 |
| url | https://arxiv.org/abs/2502.09470 |