#### Vol. 309, No. 2, 2020

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Thin subgroups isomorphic to Gromov–Piatetski-Shapiro lattices

### Samuel A. Ballas

Vol. 309 (2020), No. 2, 257–266
##### Abstract

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

##### Keywords
thin groups, nonarithmetic lattices
##### Mathematical Subject Classification 2010
Primary: 22E40, 57M50