Professor Michael Magee michael.r.magee@durham.ac.uk
Professor
Quantitative spectral gap for thin groups of hyperbolic isometries
Magee, Michael
Authors
Abstract
Let ΛΛ be a subgroup of an arithmetic lattice in SO(n+1,1)SO(n+1,1). The quotient Hn+1/ΛHn+1/Λ has a natural family of congruence covers corresponding to ideals in a ring of integers. We establish a super-strong approximation result for Zariski-dense ΛΛ with some additional regularity and thickness properties. Concretely, this asserts a quantitative spectral gap for the Laplacian operators on the congruence covers. This generalizes results of Sarnak and Xue (1991) and Gamburd (2002).
Journal Article Type | Article |
---|---|
Online Publication Date | Feb 5, 2015 |
Publication Date | Jan 1, 2015 |
Deposit Date | Sep 7, 2017 |
Publicly Available Date | Oct 24, 2017 |
Journal | Journal of the European Mathematical Society |
Print ISSN | 1435-9855 |
Electronic ISSN | 1435-9863 |
Publisher | EMS Press |
Peer Reviewed | Peer Reviewed |
Volume | 17 |
Issue | 1 |
Pages | 151-187 |
DOI | https://doi.org/10.4171/jems/500 |
Public URL | https://durham-repository.worktribe.com/output/1377038 |
Related Public URLs | https://arxiv.org/abs/1112.2004 |
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Accepted Journal Article
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