9/20/2007

Michel Boileau
Toulouse

Sequences of metrics with a local curvature bound and an asymptotically
hyperbolic thick part on aspherical 3-manifolds

We give a sufficient condition for a closed, orientable and aspherical 3-manifold to be Seifert fibred or to contain an incompressible torus. This condition relies on the existence of a sequence of Riemannian metrics whose sectional curvature is locally controlled and thick part is asymptotically hyperbolic. Perelmaqn's construction of the Ricci flow with surgery insures the existence of such sequences. Our result gives an alternative approach for the last step in Perelman's proof of the geometrization conjecture for aspherical 3-manifolds. (This is a joint work with L. Bessieres, G. Besson, S. Maillot et J. Porti)