LERF, the Lubotzky-Sarnak Conjecture and the topology of hyperbolic 3-manifolds
Alan Reid

The Lubotzky-Sarnak Conjecture asserts that the fundamental group of a finite volume hyperbolic manifold does not have Property \tau.

Put in a geometric context, this conjecture predicts a tower of finite sheeted covers for which the Cheeger constant goes to zero.  This conjecture has attracted a lot of attention recently because of its connections to the topology of finite sheeted covers of closed hyperbolic 3-manifolds.  This talk will discuss these connections, together with recent work that connects this circle of ideas with the group theoretic property LERF (a far reaching generalization of residually finite).

Colloquium, Department of Mathematics, Rice University
January 15, 2009 HB 227 4-5 PM


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