A Uniform Spectral Gap for Congruence Covers of a Hyperbolic Manifold

@inproceedings{Silberman2012AUS,
  title={A Uniform Spectral Gap for Congruence Covers of a Hyperbolic Manifold},
  author={Lior Silberman},
  year={2012}
}
Let G be SO(n, 1) or SU(n, 1) and let Γ ⊂ G denote an arithmetic lattice. The hyperbolic manifold Γ\H comes with a natural family of covers, coming from the congruence subgroups of Γ. In many applications, it is useful to have a bound for the spectral gap that is uniform for this family. When Γ is itself a congruence lattice, there are very good bounds… CONTINUE READING