Collapsing irreducible 3-manifolds with nontrivial fundamental group

@article{Bessires2009CollapsingI3,
  title={Collapsing irreducible 3-manifolds with nontrivial fundamental group},
  author={Laurent Bessi{\`e}res and G'erard Besson and Michel Boileau and Sylvain Maillot and Joan Porti},
  journal={Inventiones mathematicae},
  year={2009},
  volume={179},
  pages={435-460}
}
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. 

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