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

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