Circle-valued Morse Theory

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