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070530s2007 riua b 001 0 eng |
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|a 2007062016
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|a 0821843281 (alk. paper)
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|a 9780821843284 (alk. paper)
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|a (OCoLC)145147251
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|a 2682382
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|b .M67 2007
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|a 516.3/62
|2 22
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|a Morgan, John W.,
|d 1946-
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|a Ricci flow and the Poincar�e conjecture /
|c John Morgan, Gang Tian
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| 260 |
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|a Providence, RI :
|b American Mathematical Society :
|b Clay Mathematics Institute,
|c c2007
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| 300 |
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|a xlii, 521 p. :
|b ill. ;
|c 27 cm
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| 490 |
1 |
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|a Clay mathematics monographs,
|x 1539-6061 ;
|v v. 3
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| 504 |
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|a Includes bibliographical references (p. 515-518) and index
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| 505 |
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|g Pt. 1
|t Background from Riemannian geometry and Ricci flow --
|g Ch. 1.
|t Preliminaries from Riemannian geometry --
|g Ch. 2.
|t Manifolds of non-negative curvature --
|g Ch. 3.
|t Basics of Ricci flow --
|g Ch. 4.
|t maximum principle --
|g Ch. 5.
|t Convergence results for Ricci flow --
|g Pt. 2.
|t Perelmans length function and its applications --
|g Ch. 6.
|t comparison geometry approach to the Ricci flow --
|g Ch. 7.
|t Complete Ricci flows of bounded curvature --
|g Ch. 8.
|t Non-collapsed results --
|g Ch. 9.
|t [kappa]-non-collapsed ancient solutions --
|g Ch. 10.
|t Bounded curvature at bounded distance --
|g Ch. 11.
|t Geometric limits of generalized Ricci flows --
|g Ch. 12.
|t standard solution --
|g Pt. 3.
|t Ricci flow with surgery --
|g Ch. 13.
|t Surgery on a [delta]-neck --
|g Ch. 14.
|t Ricci flow with surgery : the definition --
|g Ch. 15.
|t Controlled Ricci flows with surgery --
|g Ch. 16.
|t Proof of non-collapsing --
|g Ch. 17.
|t Completion of the proof of Theorem 15.9 --
|g Pt. 4.
|t Completion of the proof of the Poincare conjecture --
|g Ch. 18.
|t Finite-time extinction --
|g Ch. 19.
|t Completion of the proof of proposition 18.24 --
|g App.
|t 3-manifolds covered by canonical neighborhoods.
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| 520 |
1 |
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|a 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
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|a Poincar�e conjecture
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|a Ricci flow
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|a Tian, G
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| 830 |
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|a Clay mathematics monographs ;
|v v. 3
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