Constructing thin subgroups of SL(n + 1, ℝ) via bending

Ballas, Samuel A¹ ; Long, Darren D²

¹Department of Mathematics, Florida State University, Tallahassee, FL, United States
²Department of Mathematics, University of California, Santa Barbara, Santa Barbara, CA, United States

Algebraic and Geometric Topology, Tome 20 (2020) no. 4, pp. 2071-2093

Résumé

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, ℝ) 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.

Détail

DOI : 10.2140/agt.2020.20.2071

Classification : 57M50, 22E40
Keywords: thin groups, bending, projective structures, arithmetic groups

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