Augustin Banyaga, David Hurtubise (auth.)1402026951, 9781402026959, 140202696X
This book is based on the lecture notes from a course we taught at Penn State University during the fall of 2002. The main goal of the course was to give a complete and detailed proof of the Morse Homology Theorem (Theo rem 7.4) at a level appropriate for second year graduate students. The course was designed for students who had a basic understanding of singular homol ogy, CW-complexes, applications of the existence and uniqueness theorem for O.D.E.s to vector fields on smooth Riemannian manifolds, and Sard’s Theo rem. We would like to thank the following students for their participation in the course and their help proofreading early versions of this manuscript: James Barton, Shantanu Dave, Svetlana Krat, Viet-Trung Luu, and Chris Saunders. We would especially like to thank Chris Saunders for his dedication and en thusiasm concerning this project and the many helpful suggestions he made throughout the development of this text. We would also like to thank Bob Wells for sharing with us his extensive knowledge of CW-complexes, Morse theory, and singular homology. Chapters 3 and 6, in particular, benefited significantly from the many insightful conver sations we had with Bob Wells concerning a Morse function and its associated CW-complex. |
Table of contents :
Front Matter….Pages i-ix
Introduction….Pages 1-14
The CW-Homology Theorem….Pages 15-44
Basic Morse Theory….Pages 45-91
The Stable/Unstable Manifold Theorem….Pages 93-126
Basic Differential Topology….Pages 127-155
Morse-Smale Functions….Pages 157-194
The Morse Homology Theorem….Pages 195-225
Morse Theory On Grassmann Manifolds….Pages 227-268
An Overview of Floer Homology Theories….Pages 269-286
Back Matter….Pages 287-326 |
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