Circle-valued Morse Theory / / Andrei V. Pajitnov.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Pajitnov, Andrei V.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2006
• Year of Publication: 2008
• Language: English
• Series: De Gruyter Studies in Mathematics , 32
• Physical Description: 1 online resource (454 p.)

In the early 1920s 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. Circle-valued Morse theory o...

Table of Contents

• Frontmatter
• Contents
• Preface
• Introduction
• Part 1. Morse functions and vector fields on
• manifolds
• CHAPTER 1. Vector fields and C0 topology
• CHAPTER 2. Morse functions and their
• gradients
• CHAPTER 3. Gradient flows of real-valued Morse
• functions
• Part 2. Transversality, handles, Morse
• complexes
• CHAPTER 4. The Kupka-Smale transversality theory
• for gradient flows
• CHAPTER 5. Handles
• CHAPTER 6. The Morse complex of a Morse
• function
• Part 3. Cellular gradients
• CHAPTER 7. Condition (C)
• CHAPTER 8. Cellular gradients are
• C0-generic
• CHAPTER 9. Properties of cellular gradients
• Part 4. Circle-valued Morse maps and Novikov
• complexes
• CHAPTER 10. Completions of rings, modules and
• complexes
• CHAPTER 11. The Novikov complex of a circle-valued
• Morse map
• CHAPTER 12. Cellular gradients of circle-valued
• Morse functions and the Rationality Theorem
• CHAPTER 13. Counting closed orbits of the gradient
• flow
• CHAPTER 14. Selected topics in the Morse-Novikov
• theory
• Backmatter