Geometry & Topology

LERF and the Lubotzky–Sarnak Conjecture

Marc Lackenby, Darren D Long, and Alan W Reid

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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.

Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 2047-2056.

Dates
Received: 11 April 2008
Accepted: 21 May 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800121

Digital Object Identifier
doi:10.2140/gt.2008.12.2047

Mathematical Reviews number (MathSciNet)
MR2431015

Zentralblatt MATH identifier
1157.57009

Subjects
Primary: 57M50: Geometric structures on low-dimensional manifolds

Keywords
subgroup separability Cheeger constant Lubotzky–Sarnak conjecture

Citation

Lackenby, Marc; Long, Darren D; Reid, Alan W. LERF and the Lubotzky–Sarnak Conjecture. Geom. Topol. 12 (2008), no. 4, 2047--2056. doi:10.2140/gt.2008.12.2047. https://projecteuclid.org/euclid.gt/1513800121


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