The cohomology of hyperbolic 3-manifolds
by Frank Calegari
Abstract: There exist 3-manifolds X with infinite fundamental group whose homology is that of the 3-sphere. If X is a hyperbolic 3-manifold, however, then Lubotzky explained how to find covers Y of X such that the homology H1(Y,Z/pZ) becomes arbitrarily large. Already this is enough to prove that lattices in SL2(C) do not satisfy the congruence subgroup property. In this talk, I will study the growth of H1(Y,Z/pZ) in some special towers of covers of X corresponding to p-adic analytic groups. The special case when G is the additive group of p-adic numbers will be related to the classical Alexander polynomial.
For More Information: contact: Arun Ram. email: firstname.lastname@example.org