Preface This manuscript is a slightly revised version of notes of lectures given by JM at Stanford University in the Winter and Spring Quarters of 2009 with notes taken by FF. The purpose of the course and manuscript is to provide an overview of the arguments, due almost entirely to Perelman, using Ricci flow to prove the Poincar´ e Conjecture and Thurston’s Geometrization Conjecture for 3-manifolds. The material presented here is not as complete as the treatments in [13], [10], [3], and [1], but hopefully these course notes give the interested reader insight into the structure of the arguments and some of the key ideas and will prepare him or her to tackle the more detailed treatments. We wish to thank the participants from the course, especially Eleny Ionel, Brian White, Wu-Chung Hsiang, and Steve Kerckhoff. They were diligent in their attention to the material and insightful with their questions and comments. We also thank Eleny for making her excellent class notes available as we prepared this manuscript. JM would like to thank Columbia University for sabbatical support during the academic year 2008-2009 and Stanford University for hospitality and their support during this year and to especially thank Yakov Eliashberg for arranging the sabbat- ical visit. JM found it a great pleasure both intellectually and personally to spend a year at Stanford. FF would like to thank Stanford University and his advisor Prof. Richard Schoen for providing him research assistantship. He would also like to thank JM who delivered wonderful lectures on this subject and guided us through the proof of these conjectures. This work was partially supported by NSF grant DMS/0706815 and grant DMS/0604960. John W. Morgan Frederick Tsz-Ho Fong ix
Previous Page Next Page