LERF, the Lubotzky-Sarnak Conjecture and the Topology of Hyperbolic 3-Manifolds

MEMBERS SEMINAR
Topic:LERF, the Lubotzky-Sarnak Conjecture and the Topology of Hyperbolic 3-Manifolds
Speaker:Alan Reid
Affiliation:The University of Texas at Austin and Member, School of Mathematics
Date:Monday, November 10
Time/Room:2:00pm - 3:00pm/S-101

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 these circles of ideas with the group theoretic property LERF (a far reaching generalization of residually finite).