Completion of the Proof of the Geometrization Conjecture
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 threemanifolds 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.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 arXiv:
 arXiv:0809.4040
 Bibcode:
 2008arXiv0809.4040M
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Geometric Topology;
 53C20;
 53C21: 53C23
 EPrint:
 84 pages