### Integral homology of hyperbolic three--manifolds

- Series
- Geometry Topology Seminar
- Time
- Friday, April 5, 2013 - 14:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Jean Raimbault – Institut de Mathematiques de Jussieu, Universite Pierre et Marie Curie

It is a natural question to ask whether one can deduce topological
properties of a finite--volume three--manifold from its Riemannian
invariants such as volume and systole. In all generality this is
impossible, for example a given manifold has sequences of finite covers
with either linear or sub-linear growth. However under a geometric
assumption, which is satisfied for example by some naturally defined
sequences of arithmetic manifolds, one can prove results on the
asymptotics of the first integral homology. I will try to explain these
results in the compact case (this is part of a joint work with M. Abert,
N. Bergeron, I. Biringer, T. Gelander, N. Nikolov and I. Samet) and time
permitting I will discuss their extension to manifolds with cusps such
as hyperbolic knot complements.