The geometrization conjecture

著者

• Morgan, John W.
• Tian, G.

書誌事項

The geometrization conjecture

John Morgan, Gang Tian

（Clay mathematics monographs, v. 5）

American Mathematical Society , Clay Mathematics Institute, c2014

注記

Includes bibliographical references (p. 281-282) and index

内容説明・目次

内容説明

This book gives a complete proof of the geometrization conjecture, which describes all compact 3-manifolds in terms of geometric pieces, i.e., 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-manifolds are Alexandrov spaces of dimension at most 2 and then classifying these Alexandrov spaces. In the course of proving the geometrization conjecture, the authors provide an overview of the main results about Ricci flows with surgery on 3-dimensional manifolds, introducing the reader to this difficult material. The book also includes an elementary introduction to Gromov-Hausdorff limits and to the basics of the theory of Alexandrov spaces. In addition, a complete picture of the local structure of Alexandrov surfaces is developed. All of these important topics are of independent interest.

目次

Introduction Geometric and analytic results for Ricci flow with surgery Ricci flow with surger Limits as t?? Local results valid for large time Proofs of the three propositions Locally volume collapsed 3-manifolds Introduction to part II The collapsing theorem Overview of the rest of the argument Basics of Gromov-Hausdorff convergence Basics of Alexandrov spaces 2-dimensional Alexandrov spaces 3-dimensional analogues The global result The equivariant case The equivariant case Bibliography Glossary of symbols Index

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詳細情報

• NII書誌ID(NCID): BB15765385
• ISBN:
  • 9780821852019
• LCCN: 2013045837
• 出版国コード: us
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Providence, R.I.,Cambridge, Mass.
• ページ数/冊数: ix, 291 p.
• 大きさ: 26 cm
• 分類:
  • LCC : QA671
  • DC23 : 516.3/62
• 件名:
  • LCSH : Global Riemannian geometry
  • LCSH : Topological manifolds
• 親書誌ID:
  • BA63790513