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(n,1, ) constructed by Gromov and Piatetski-Shapiro can be embedded into SL(n + 1, ) 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
Authors
Samuel A. Ballas
Department of Mathematics
Florida State University
Tallahassee, FL
United States