Lectures on Morse Homology

Augustin Banyaga, David Hurtubise (Autoren)

Buch | Softcover

326 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2004
Springer (Verlag)
978-90-481-6705-0 (ISBN)

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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.

1. Introduction.- 2. The CW-Homology Theorem.- 3. Basic Morse Theory.- 4. The Stable/Unstable Manifold Theorem.- 5. Basic Differential Topology.- 6. Morse-Smale Functions.- 7. The Morse Homology Theorem.- 8. Morse Theory On Grassmann Manifolds.- 9. An Overview of Floer Homology Theories.- Hints and References for Selected Problems.- Symbol Index.

Erscheint lt. Verlag	8.12.2010
Reihe/Serie	Texts in the Mathematical Sciences ; 29
Zusatzinfo	IX, 326 p.
Verlagsort	Dordrecht
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	90-481-6705-1 / 9048167051
ISBN-13	978-90-481-6705-0 / 9789048167050
Zustand	Neuware