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
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
John W. Morgan
Frederick Tsz-Ho Fong
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