This is a joint work with **Laurent Bessières**, **Michel Boileau**, **Sylvain Maillot** and **Joan Porti**. Let M be a closed, orientable, irreducible, non-simply connected 3-manifold.We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman’s proof of Thurston’s Geometrisation Conjecture.

The reference is:

L. Bessières, G. Besson, M. Boileau, S. Maillot and J. Porti *Collapsing irreducible 3-manifolds with nontrivial fundamental group * Invent math (2010) 179: 435–460.

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