A hyperbolic lattice in each dimension with Zariski-dense surface subgroups

Abstract

For each integer $n\ge 3$, we exhibit a nonuniform arithmetic lattice in $\mathrm{SO}(n,1)$ containing Zariski-dense surface subgroups.

Typos in the proofs of Lemma 2 and Theorem 1 were corrected, and a remark was appended to account for more straightforward examples in even dimensions. 5 pages, 1 figure