Geometry & Topology
- Geom. Topol.
- Volume 12, Number 4 (2008), 2047-2056.
LERF and the Lubotzky–Sarnak Conjecture
We prove that every closed hyperbolic –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.
Geom. Topol., Volume 12, Number 4 (2008), 2047-2056.
Received: 11 April 2008
Accepted: 21 May 2008
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 57M50: Geometric structures on low-dimensional manifolds
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