LERF and the Lubotzky–Sarnak Conjecture

Marc Lackenby; Darren D Long; Alan W Reid

doi:10.2140/gt.2008.12.2047

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Home > Journals > Geom. Topol. > Volume 12 > Issue 4 > Article

2008 LERF and the Lubotzky–Sarnak Conjecture

Marc Lackenby, Darren D Long, Alan W Reid

Geom. Topol. 12(4): 2047-2056 (2008). DOI: 10.2140/gt.2008.12.2047

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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.

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Marc Lackenby. Darren D Long. Alan W Reid. "LERF and the Lubotzky–Sarnak Conjecture." Geom. Topol. 12 (4) 2047 - 2056, 2008. https://doi.org/10.2140/gt.2008.12.2047