# Quantitative spectral gap for thin groups of hyperbolic isometries

Journal of the European Mathematical Society (2015)

- Volume: 017, Issue: 1, page 151-187
- ISSN: 1435-9855

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topMagee, Michael. "Quantitative spectral gap for thin groups of hyperbolic isometries." Journal of the European Mathematical Society 017.1 (2015): 151-187. <http://eudml.org/doc/277362>.

@article{Magee2015,

abstract = {Let $\Lambda $ be a subgroup of an arithmetic lattice in $\mathrm \{SO\}(n+1 , 1)$. The quotient $\mathbb \{H\}^\{n+1\} / \Lambda $ 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 $\Lambda $ 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).},

author = {Magee, Michael},

journal = {Journal of the European Mathematical Society},

keywords = {spectral gap; thin groups; hyperbolic manifold; Laplacian operator; spectral gap; thin groups; hyperbolic manifold; Laplacian operator},

language = {eng},

number = {1},

pages = {151-187},

publisher = {European Mathematical Society Publishing House},

title = {Quantitative spectral gap for thin groups of hyperbolic isometries},

url = {http://eudml.org/doc/277362},

volume = {017},

year = {2015},

}

TY - JOUR

AU - Magee, Michael

TI - Quantitative spectral gap for thin groups of hyperbolic isometries

JO - Journal of the European Mathematical Society

PY - 2015

PB - European Mathematical Society Publishing House

VL - 017

IS - 1

SP - 151

EP - 187

AB - Let $\Lambda $ be a subgroup of an arithmetic lattice in $\mathrm {SO}(n+1 , 1)$. The quotient $\mathbb {H}^{n+1} / \Lambda $ 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 $\Lambda $ 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).

LA - eng

KW - spectral gap; thin groups; hyperbolic manifold; Laplacian operator; spectral gap; thin groups; hyperbolic manifold; Laplacian operator

UR - http://eudml.org/doc/277362

ER -

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