Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$

Sara Edelman-Muñoz; Michael Zshornack

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arXiv · 2605.11129

Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$

Sara Edelman-Muñoz·Michael Zshornack

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Abstract

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 $\rm{SO}^+(n+1,1)$.

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Sara Edelman-Muñoz, Michael Zshornack. 2026-05-11. Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$. https://arxiv.org/abs/2605.11129

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