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2020 Constructing thin subgroups of $\mathrm{SL}(n+1,\mathbb{R})$ via bending
Samuel A Ballas, Darren D Long
Algebr. Geom. Topol. 20(4): 2071-2093 (2020). DOI: 10.2140/agt.2020.20.2071

Abstract

We use techniques from convex projective geometry to produce many new examples of thin subgroups of lattices in special linear groups that are isomorphic to the fundamental groups of finite-volume hyperbolic manifolds. More specifically, we show that for a large class of arithmetic lattices in SO(n,1) it is possible to find infinitely many noncommensurable lattices in SL(n+1,) that contain a thin subgroup isomorphic to a finite-index subgroup of the original arithmetic lattice. This class of arithmetic lattices includes all noncocompact arithmetic lattices as well as all cocompact arithmetic lattices when n is even.

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Samuel A Ballas. Darren D Long. "Constructing thin subgroups of $\mathrm{SL}(n+1,\mathbb{R})$ via bending." Algebr. Geom. Topol. 20 (4) 2071 - 2093, 2020. https://doi.org/10.2140/agt.2020.20.2071

Information

Received: 22 March 2019; Revised: 28 October 2019; Accepted: 21 November 2019; Published: 2020
First available in Project Euclid: 1 August 2020

zbMATH: 07226711
MathSciNet: MR4127090
Digital Object Identifier: 10.2140/agt.2020.20.2071

Subjects:
Primary: 57M50
Secondary: 22E40

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.20 • No. 4 • 2020
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