English

LERF and the Lubotzky-Sarnak conjecture

Geometric Topology 2008-04-09 v1 Differential Geometry

Abstract

We prove that every closed hyperbolic 3-manifold has a family of (possibly infinite sheeted) coverings with the property that the Cheeger constants in the family tend to zero. This is used to show that, if in addition the fundamental group of the manifold is LERF, then it satisfies the Lubotzky-Sarnak conjecture.

Keywords

Cite

@article{arxiv.0804.1305,
  title  = {LERF and the Lubotzky-Sarnak conjecture},
  author = {M. Lackenby and D. D. Long and A. W. Reid},
  journal= {arXiv preprint arXiv:0804.1305},
  year   = {2008}
}

Comments

9 pages

R2 v1 2026-06-21T10:28:53.529Z