Convex cocompact groups with three-dimensional limit sets
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910092985630720 |
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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 provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary simplicial complex L of dimension 3 on n vertices, and outputs a convex cocompact right-angled reflection group acting on real hyperbolic n-space whose nerve is precisely the Przytycki-Świątkowski subdivision of L. Moreover, the output reflection group is a thin subgroup of an n-dimensional cocompact arithmetic hyperbolic lattice. This answers affirmatively a question of M. Kapovich concerning the existence of a convex cocompact group acting on some real hyperbolic space with limit set a Čech cohomology sphere other than the standard sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00466 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Convex cocompact groups with three-dimensional limit sets Douba, Sami Lee, Gye-Seon Marquis, Ludovic Ruffoni, Lorenzo Group Theory Geometric Topology 20F65, 20F67, 22E40 (Primary) 20F55 (Secondary) We provide a general construction of convex cocompact hyperbolic reflection groups with three-dimensional limit sets. More precisely, our construction takes as input an arbitrary simplicial complex L of dimension 3 on n vertices, and outputs a convex cocompact right-angled reflection group acting on real hyperbolic n-space whose nerve is precisely the Przytycki-Świątkowski subdivision of L. Moreover, the output reflection group is a thin subgroup of an n-dimensional cocompact arithmetic hyperbolic lattice. This answers affirmatively a question of M. Kapovich concerning the existence of a convex cocompact group acting on some real hyperbolic space with limit set a Čech cohomology sphere other than the standard sphere. |
| title | Convex cocompact groups with three-dimensional limit sets |
| topic | Group Theory Geometric Topology 20F65, 20F67, 22E40 (Primary) 20F55 (Secondary) |
| url | https://arxiv.org/abs/2604.00466 |