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