Quantitative spectral gap for thin groups of hyperbolic isometries

Magee, Michael

doi:10.4171/jems/500

Quantitative spectral gap for thin groups of hyperbolic isometries

Magee, Michael

Authors

Professor Michael Magee michael.r.magee@durham.ac.uk
Professor

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).

Citation

Magee, M. (2015). Quantitative spectral gap for thin groups of hyperbolic isometries. Journal of the European Mathematical Society, 17(1), 151-187. https://doi.org/10.4171/jems/500

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
Related Public URLs	https://arxiv.org/abs/1112.2004