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

Sara Edelman-Muñoz; Michael Zshornack

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

Geometric Topology 2026-05-13 v1 Group Theory

Authors: Sara Edelman-Muñoz , Michael Zshornack

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

Keywords

surface subgroups arithmetic lattices hyperbolic manifolds fundamental group GFERF

Cite

@article{arxiv.2605.11129,
  title  = {Thin surface subgroups of non-uniform arithmetic lattices in $\rm{SO}^+(n,1)$},
  author = {Sara Edelman-Muñoz and Michael Zshornack},
  journal= {arXiv preprint arXiv:2605.11129},
  year   = {2026}
}

Comments

20 pages, 9 figures, comments welcome

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