Thin subgroups isomorphic to Gromov--Piatetski-Shapiro lattices

Abstract

In this paper we produce many examples of thin subgroups of special linear groups that are isomorphic to the fundamental groups of non-arithmetic hyperbolic manifolds. Specifically, we show that the non-arithmetic lattices in $\mathrm{SO}(n,1)$ constructed by Gromov and Piatetski-Shapiro can be embedded into ${\mathrm{SL}}_{n+1}(\mathbb{R})$ so that their images are thin subgroups

v3: 7 pages, 1 figure, final version to appear in Pacific J Math