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Completion of the Proof of the Geometrization Conjecture

Authors
  • Morgan, John
  • Tian, Gang
Type
Preprint
Publication Date
Sep 23, 2008
Submission Date
Sep 23, 2008
Identifiers
arXiv ID: 0809.4040
Source
arXiv
License
Yellow
External links

Abstract

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.

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