Abstract
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. © Springer-Verlag 2009.
Original language | English |
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Pages (from-to) | 435-460 |
Journal | Inventiones Mathematicae |
Volume | 179 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1 Dec 2009 |