Completion of the Proof of the Geometrization Conjecture
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This article is a sequel to the book `Ricci Flow and the Poincare Conjecture' by the same authors. Using the main results of that book we establish the Geometrization Conjecture for all compact, orientable three-manifolds following the approach indicated by Perelman in his preprints on the subject. This approach is to study the collapsed part of the manifold as time goes to infinity in a Ricci flow with surgery. The main technique for this study is the theory of Alexandrov spaces. This theory gives local models for the collapsed part of the manifold. These local models can be glued together to prove that the collapsed part of the manifold is a graph manifold with incompressible boundary. From this and previous results, geometrization follows easily.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/f7c1fa78dc2782d7c7c938fae915adf5f9d668a3
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds (2008, background): “Since M0 is not a graph manifold, the thick parts of the time slices Mt cannot be empty for large t, cf. [15, Sections 89 and 92] and [ 21, Theorem 0.2 ].”
- Geometrisation of 3-Manifolds (2010, background): “We warmly thank B. Kleiner, J. Lott, J. Morgan and G. Tian for numerous fruitful exchanges.”
- Ricci flow coupled with harmonic map flow (2009, background): “More advanced explanations of Perelman’s proof of the two conjectures are given in Cao and Zhu [3] Chow et al. [5, 6], Kleiner and Lott [19] and Morgan and Tian [25, 26].”
- The minimal volume orientable hyperbolic 2-cusped 3-manifolds (2008, background): “The arguments of [2, 3] depend strongly on Perelman’s proof of the geometrization conjecture (see [19, 18, 12, 14, 6, 15]).”