Thin subgroups isomorphic to Gromov–Piatetski-Shapiro lattices

Samuel A. Ballas

Vol. 309 (2020), No. 2, 257–266

DOI: 10.2140/pjm.2020.309.257

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

Milestones

Received: 18 November 2019

Revised: 23 November 2020

Accepted: 24 November 2020

Published: 14 January 2021