000			02300nam a22002537a 4500
003			OSt
005			20250103110747.0
008			190226b ||||| |||| 00| 0 eng d
020			_a9781402026959
040			_cTata Book House _aICTS-TIFR
050			_aQA331
100			_aAugustin Banyaga
245			_aLectures on Morse Homology
260			_aBoston: _bKluwer Academic Publisher, _c[c2004]
300			_a324 p
490			_aTexts in the Mathematical Sciences _vVol. 29
505			_a1. 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
520			_aThis 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. --- summary provided by publisher
650			_aAlgebraic topology
650			_aOrdinary differential equations
700			_aDavid Hurtubise
856			_uhttps://link.springer.com/book/10.1007/978-1-4020-2696-6#keywords
942			_2lcc _cBK
999			_c2403 _d2403