Quantitative spectral gap for thin groups of hyperbolic isometries

Magee, 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 -