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

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