Circle-valued Morse Theory (eBook)

Andrei V. Pajitnov (Autor)

eBook Download: PDF

2006
463 Seiten
De Gruyter (Verlag)
978-3-11-019797-6 (ISBN)

Infos

In 1927 M. Morse discovered that the number of critical points of a smooth function on a manifold is closely related to the topology of the manifold. This became a starting point of the Morse theory which is now one of the basic parts of differential topology. It is a large and actively developing domain of differential topology, with applications and connections to many geometrical problems. The aim of the present book is to give a systematic treatment of the geometric foundations of a subfield of that topic, the circle-valued Morse functions, a subfield of Morse theory.

Andrei Pajitnov, University of Nantes, France.

Autor

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Andrei Pajitnov, University of Nantes, France.

Inhalt

Frontmatter 1
Contents 7
Preface 11
Introduction 15
CHAPTER 1. Vector fields and C0 topology 27
CHAPTER 2. Morse functions and their gradients 43
CHAPTER 3. Gradient flows of real-valued Morse functions 77
CHAPTER 4. The Kupka-Smale transversality theory for gradient flows 121
CHAPTER 5. Handles 173
CHAPTER 6. The Morse complex of a Morse function 205
CHAPTER 7. Condition (C) 241
CHAPTER 8. Cellular gradients are C0-generic 253
CHAPTER 9. Properties of cellular gradients 291
CHAPTER 10. Completions of rings, modules and complexes 335
CHAPTER 11. The Novikov complex of a circle-valued Morse map 345
CHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem 377
CHAPTER 13. Counting closed orbits of the gradient flow 393
CHAPTER 14. Selected topics in the Morse-Novikov theory 423
Backmatter 445

Rezensionen

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"Overall the book covers a lot of material in a style and detail that should be easily accessible to both graduate students and researchers wanting to learn the subject."
Dirk Schütz in: Mathematical Reviews 2008

"The book under review is a very nice and valuable text on the Morse-Novikov theory. It can help anyone who wants to learn the basis of the theory as well as some more recent and advanced developments and applications."
Davod Chataur in: Zentralblatt MATH 1118/2007

Produkt-Details

• Erscheint lt. Verlag: 22.8.2008
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: De Gruyter Studies in Mathematics
• Reihe/Serie: ISSN
• Reihe/Serie: ISSN
• Verlagsort: Berlin/Boston
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
• Themenwelt: Technik
• Schlagworte: Differentialgeometrie • Differential Geometry • Differential geometry; Morse theory • Morsetheorie • Morse Theory
• ISBN-10: 3-11-019797-9 / 3110197979
• ISBN-13: 978-3-11-019797-6 / 9783110197976