Thin subgroups isomorphic to Gromov-Piateski-Shapiro lattices

Samuel A. Ballas

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 SO(n,1,R) constructed by Gromov and Piateski-Shapiro can be embedded into SL(n+1,R) so that their images are thin subgroups.