# The cohomology of hyperbolic 3-manifolds

*Algebra/Geometry/Topology Seminar*

*by Frank Calegari*

*Institution:*Northwestern University, USA

*Date: Thu 16th June 2011*

*Time: 2:00 PM*

*Location: Room 215, Richard Berry Building, The University of Melbourne*

*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: aram@unimelb.edu.au