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

Abstract

We show that the fundamental groups of all non-compact, arithmetic, hyperbolic, $n$-manifolds for $n\ge 4$ 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 ${\mathrm{SO}}^{+}(\mathrm{n}+1,1)$.

arXiv comment20 pages, 9 figures, comments welcome