Contents
Preface ix
Part 1. Overview 1
Lecture 1 3
Geometric manifolds 3
Thurston manifolds 4
The theorems 5
Lecture 2 7
Basics of Riemannian geometry 7
Basics of Ricci flow 8
Canonical Neighborhoods 10
Lecture 3 13
More on Canonical Neighborhoods 13
Surgery on Ricci flow 14
Topological effects of surgery 16
Lecture 4 17
More structure (geometric and analytic) of Canonical Neighborhoods 17
Finite-time extinction 18
Lecture 5 21
Geometric limits 21
Hyperbolic limits 22
The thin part 23
Alexandrov spaces 23
Summary of Part 1 25
Part 2. Non-collapsing Results for Ricci Flows 27
Lecture 6 29
Geometric limits in the context of Ricci flow 29
Sketch of proof of the convergence theorem 31
Lecture 7 33
Non-collapsing: the statement 33
The L-function and L-geodesics 34
Lecture 8 37
v
Previous Page Next Page