Ricci Flow and Geometrization of 3-Manifolds
About this Title
John W. Morgan, Stony Brook University, Stony Brook, NY and Frederick Tsz-Ho Fong, Stanford University, Stanford, CA
Publication: University Lecture Series
Publication Year 2010: Volume 53
ISBNs: 978-0-8218-4963-7 (print); 978-1-4704-1648-5 (online)
MathSciNet review: MR2597148
MSC: Primary 53C44; Secondary 53C21, 57M40, 57M50, 57N10
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 3-dimensional manifolds. Most of the material is geometric and analytic in nature; a crucial ingredient is understanding singularity development for 3-dimensional Ricci flows and for 3-dimensional 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 time-slices 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.
Table of Contents
Part 1. Overview
Part 2. Non-collapsing results for Ricci flows
Part 3. $\kappa $-solutions
Part 4. The canonical neighborhood theorem
Part 5. Ricci flow with surgery
Part 6. Behavior as $t \to \infty $