%0 Journal Article
%T Weak collapsing and geometrisation of aspherical 3-manifolds
%A Laurent Bessi¨¨res
%A G¨¦rard Besson
%A Michel Boileau
%A Sylvain Maillot
%A Joan Porti
%J Mathematics
%D 2007
%I arXiv
%X Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics whose sectional curvature is locally controlled and whose thick part becomes asymptotically hyperbolic and has a sufficiently small volume, then M is Seifert fibred or contains an incompressible torus. This result gives an alternative approach for the last step in Perelman's proof of the Geometrisation Conjecture for aspherical 3-manifolds.
%U http://arxiv.org/abs/0706.2065v2