Circle-valued Morse Theory (eBook)

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Andrei Pajitnov, University of Nantes, France.

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

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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