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.
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Bessières, L., Besson, G., Boileau, M. et al. Collapsing irreducible 3-manifolds with nontrivial fundamental group. Invent. math. 179, 435–460 (2010). https://doi.org/10.1007/s00222-009-0222-6
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DOI: https://doi.org/10.1007/s00222-009-0222-6