Sequences of metrics given by the long term Ricci Flow on aspherical 3-manifolds

Michel Boileau, Université Paul Sabatier, Toulouse, France

Abstract: 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 is the existence of a sequence of Riemannian metrics
having various properties, in particular its sectional curvature is locally
controlled and its thick part is asymptotically hyperbolic. The construction
of the Ricci flow with surgery given by G. Perelman 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. Bessières, G. Besson, S. Maillot and J. Porti)