Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917481888612352 |
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| author | Edelman-Muñoz, Sara Zshornack, Michael |
| author_facet | Edelman-Muñoz, Sara Zshornack, Michael |
| contents | We show that the fundamental groups of all non-compact, arithmetic, hyperbolic, $n$-manifolds for $n\geq 4$ contain thin surface subgroups. As a consequence of the proof of this theorem we also show that the fundamental groups of the doubles of cusped, arithmetic, hyperbolic $n$-manifolds embed as GFERF subgroups of $\rm{SO}^+(n+1,1)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_11129 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$ Edelman-Muñoz, Sara Zshornack, Michael Geometric Topology Group Theory 57K20 We show that the fundamental groups of all non-compact, arithmetic, hyperbolic, $n$-manifolds for $n\geq 4$ contain thin surface subgroups. As a consequence of the proof of this theorem we also show that the fundamental groups of the doubles of cusped, arithmetic, hyperbolic $n$-manifolds embed as GFERF subgroups of $\rm{SO}^+(n+1,1)$. |
| title | Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$ |
| topic | Geometric Topology Group Theory 57K20 |
| url | https://arxiv.org/abs/2605.11129 |