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Constructing thin
subgroups of $\mathrm{SL}(n+1,\mathbb{R})$ via bending
Samuel A Ballas and Darren D Long |
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Algebraic & Geometric Topology 20 (2020) 2071–2093
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Abstract |
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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 it is possible to find infinitely many noncommensurable lattices in 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 is even. |
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Keywords
thin groups, bending, projective structures, arithmetic
groups
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Mathematical Subject Classification 2010
Primary: 57M50
Secondary: 22E40
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References |
Publication
Received: 22 March 2019
Revised: 28 October 2019
Accepted: 21 November 2019
Published: 20 July 2020
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Authors |
| Samuel A Ballas | |
| Department of Mathematics Florida State University Tallahassee, FL United States |
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| Darren D Long | |
| Department of Mathematics University of California, Santa Barbara Santa Barbara, CA United States |
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