The Geometrization Conjecture Morgan Tian Hardback MP–AMM American Mathematical

The Geometrization ConjectureAuthor(s): John Morgan, Gang Tian\nFormat: Hardback\nPublisher: American Mathematical Society, United States\nImprint: American Mathematical Society\nISBN-13: 9780821852019, 978-0821852019\nSynopsis\nThis book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, [url] 3-manifolds with locally homogeneous metrics of finite volume. The method is to understand the limits as time goes to infinity of Ricci flow with surgery. The first half of the book is devoted to showing that these limits divide naturally along incompressible tori into pieces on which the metric is converging smoothly to hyperbolic metrics and pieces that are locally more and more volume collapsed. The second half of the book is devoted to showing that the latter pieces are themselves geometric. This is established by showing that the Gromov-Hausdorff limits of sequences of more and more locally volume collapsed 3-mani.