Topology and Number Theory Seminar 

10/24/2002

Nicolas Bergeron
Orsay, France

We state new conjecture, of Lefschetz type, on the relationships between the (co-)homology of real and complex hyperbolic arithmetic manifolds and their totally geodesic subspaces. We prove particular cases of these conjectures by relating them to conjectures jointly made with L. Clozel on the automorphic spectrum of real and complex hyperbolic arithmetic manifolds which appear to be particular cases of the Arthur conjecture and to which we give some new approximations.