LERF and the Lubotzky-Sarnak conjecture

Details LERF and the Lubotzky-Sarnak conjecture LERF and the Lubotzky-Sarnak conjecture

2008-04-08

arxiv.org/abs/0804.1305v1

Mathematics

Geometric Topology

9 pages

Scientific paper

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.

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