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＜電子ブック＞
Lectures on Morse Homology / by Augustin Banyaga, David Hurtubise
(Texts in the Mathematical Sciences ; 29)

版	1st ed. 2004.
出版者	(Dordrecht : Springer Netherlands : Imprint: Springer)
出版年	2004
本文言語	英語
大きさ	X, 326 p : online resource
著者標目	*Banyaga, Augustin author Hurtubise, David author SpringerLink (Online service)
件　名	LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Algebraic topology LCSH:Differential equations LCSH:Topological groups LCSH:Lie groups FREE:Global Analysis and Analysis on Manifolds FREE:Manifolds and Cell Complexes FREE:Algebraic Topology FREE:Differential Equations FREE:Topological Groups and Lie Groups
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-1-4020-2696-6

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