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G&T Monographs |
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LERF and the Lubotzky–Sarnak Conjecture
Marc Lackenby, Darren D Long and Alan W Reid
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Geometry & Topology 12 (2008)
2047–2056
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Abstract
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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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Keywords
subgroup separability, Cheeger constant,
Lubotzky–Sarnak conjecture
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Mathematical Subject Classification
Primary: 57M50
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Publication
Received: 11 April 2008
Accepted: 21 May 2008
Published: 24 July 2008
Proposed: Walter Neumann
Seconded: Jean-Pierre Otal, Cameron Gordon
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