CONTENTS vii 5. Perelman's Riemannian formalism in potentially infinite dimensions 417 6. Notes and commentary 432 Chapter 9. Basic Topology of 3-Manifolds 433 1. Essential 2-spheres and irreducible 3-manifolds 433 2. Incompressible surfaces and the geometrization conjecture 435 3. Decomposition theorems and the Ricci flow 439 4. Notes and commentary 442 Appendix A. Basic Ricci Flow Theory 445 1. Riemannian geometry 445 2. Basic Ricci flow 456 3. Basic singularity theory for Ricci flow 465 4. More Ricci flow theory and ancient solutions 470 5. Classical singularity theory 474 Appendix B. Other Aspects of Ricci Flow and Related Flows 477 1. Convergence to Ricci solitons 477 2. The mean curvature flow 482 3. The cross curvature flow 490 4. Notes and commentary 500 Appendix C. Glossary 501 Bibliography 513 Index 531
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