LERF and the Lubotzky–Sarnak Conjecture

Lackenby, Marc¹ ; Long, Darren D² ; Reid, Alan W³

¹ Mathematical Institute, University of Oxford, 24-29 St Giles’, Oxford OX1 3LB, UK
² Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
³ Department of Mathematics, University of Texas, Austin, TX 78712, USA

Geometry & topology, Tome 12 (2008) no. 4, pp. 2047-2056.

Résumé

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.

Détail

DOI : 10.2140/gt.2008.12.2047

Keywords: subgroup separability, Cheeger constant, Lubotzky–Sarnak conjecture

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