Ricci flow and the Poincar�e conjecture /
This book provides full details of a complete proof of the Poincare Conjecture following Perelmans three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, i...
| Main Author: | |
|---|---|
| Other Authors: | |
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI :
American Mathematical Society : Clay Mathematics Institute,
c2007
|
| Series: | Clay mathematics monographs ;
v. 3 |
| Subjects: |
| Summary: | This book provides full details of a complete proof of the Poincare Conjecture following Perelmans three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamiltons work. The second part starts with Perelmans length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelmans third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjecture are then immediate. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology.--BOOK JACKET |
|---|---|
| Physical Description: | xlii, 521 p. : ill. ; 27 cm |
| Bibliography: | Includes bibliographical references (p. 515-518) and index |
| ISBN: | 0821843281 (alk. paper) 9780821843284 (alk. paper) |
| ISSN: | 1539-6061 ; |