Softcover ISBN:  9780821849637 
Product Code:  ULECT/53 
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AMS Member Price:  $37.60 
Electronic ISBN:  9781470416485 
Product Code:  ULECT/53.E 
List Price:  $44.00 
MAA Member Price:  $39.60 
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Book DetailsUniversity Lecture SeriesVolume: 53; 2010; 150 ppMSC: Primary 57; Secondary 35; 53;
This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincaré Conjecture and the more general Geometrization Conjecture for 3dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3dimensional Ricci flows and for 3dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the timeslices as the time goes to infinity in order to deduce the topological consequences.
The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of the same material.ReadershipGraduate students and research mathematicians interested in differential equations and topology.

Table of Contents

Part 1. Overview

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Summary of Part 1

Part 2. Noncollapsing results for Ricci flows

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Part 3. $\kappa $solutions

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Part 4. The canonical neighborhood theorem

Lecture 20

Lecture 21

Lecture 22

Part 5. Ricci flow with surgery

Lecture 23

Lecture 24

Lecture 25

Lecture 26

Part 6. Behavior as $t \to \infty $

Lecture 27

Lecture 28

Lecture 29

Lecture 30

Lecture 31

Lecture 32


Additional Material

Reviews

The notes will be useful for readers looking for an overview of the arguments and key ideas, before proceeding to the detailed proofs.
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This book is based on lectures given at Stanford University in 2009. The purpose of the lectures and of the book is to give an introductory overview of how to use Ricci flow and Ricci flow with surgery to establish the Poincaré Conjecture and the more general Geometrization Conjecture for 3dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3dimensional Ricci flows and for 3dimensional Ricci flows with surgery. This understanding is crucial for extending Ricci flows with surgery so that they are defined for all positive time. Once this result is in place, one must study the nature of the timeslices as the time goes to infinity in order to deduce the topological consequences.
The goal of the authors is to present the major geometric and analytic results and themes of the subject without weighing down the presentation with too many details. This book can be read as an introduction to more complete treatments of the same material.
Graduate students and research mathematicians interested in differential equations and topology.

Part 1. Overview

Lecture 1

Lecture 2

Lecture 3

Lecture 4

Lecture 5

Summary of Part 1

Part 2. Noncollapsing results for Ricci flows

Lecture 6

Lecture 7

Lecture 8

Lecture 9

Lecture 10

Lecture 11

Lecture 12

Part 3. $\kappa $solutions

Lecture 13

Lecture 14

Lecture 15

Lecture 16

Lecture 17

Lecture 18

Lecture 19

Part 4. The canonical neighborhood theorem

Lecture 20

Lecture 21

Lecture 22

Part 5. Ricci flow with surgery

Lecture 23

Lecture 24

Lecture 25

Lecture 26

Part 6. Behavior as $t \to \infty $

Lecture 27

Lecture 28

Lecture 29

Lecture 30

Lecture 31

Lecture 32

The notes will be useful for readers looking for an overview of the arguments and key ideas, before proceeding to the detailed proofs.
Mathematical Reviews