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CHAPTER 1. Vector fields and C0 topology

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Circle-valued Morse Theory
This chapter is in the book Circle-valued Morse Theory

Chapters in this book

  1. Frontmatter I
  2. Contents VII
  3. Preface 1
  4. Introduction 5
  5. Part 1. Morse functions and vector fields on manifolds
  6. CHAPTER 1. Vector fields and C0 topology 17
  7. CHAPTER 2. Morse functions and their gradients 33
  8. CHAPTER 3. Gradient flows of real-valued Morse functions 67
  9. Part 2. Transversality, handles, Morse complexes
  10. CHAPTER 4. The Kupka-Smale transversality theory for gradient flows 111
  11. CHAPTER 5. Handles 163
  12. CHAPTER 6. The Morse complex of a Morse function 195
  13. Part 3. Cellular gradients
  14. CHAPTER 7. Condition (C) 231
  15. CHAPTER 8. Cellular gradients are C0-generic 243
  16. CHAPTER 9. Properties of cellular gradients 281
  17. Part 4. Circle-valued Morse maps and Novikov complexes
  18. CHAPTER 10. Completions of rings, modules and complexes 325
  19. CHAPTER 11. The Novikov complex of a circle-valued Morse map 335
  20. CHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem 367
  21. CHAPTER 13. Counting closed orbits of the gradient flow 383
  22. CHAPTER 14. Selected topics in the Morse-Novikov theory 413
  23. Backmatter 435
https://doi.org/10.1515/9783110197976.1.17

Chapters in this book

  1. Frontmatter I
  2. Contents VII
  3. Preface 1
  4. Introduction 5
  5. Part 1. Morse functions and vector fields on manifolds
  6. CHAPTER 1. Vector fields and C0 topology 17
  7. CHAPTER 2. Morse functions and their gradients 33
  8. CHAPTER 3. Gradient flows of real-valued Morse functions 67
  9. Part 2. Transversality, handles, Morse complexes
  10. CHAPTER 4. The Kupka-Smale transversality theory for gradient flows 111
  11. CHAPTER 5. Handles 163
  12. CHAPTER 6. The Morse complex of a Morse function 195
  13. Part 3. Cellular gradients
  14. CHAPTER 7. Condition (C) 231
  15. CHAPTER 8. Cellular gradients are C0-generic 243
  16. CHAPTER 9. Properties of cellular gradients 281
  17. Part 4. Circle-valued Morse maps and Novikov complexes
  18. CHAPTER 10. Completions of rings, modules and complexes 325
  19. CHAPTER 11. The Novikov complex of a circle-valued Morse map 335
  20. CHAPTER 12. Cellular gradients of circle-valued Morse functions and the Rationality Theorem 367
  21. CHAPTER 13. Counting closed orbits of the gradient flow 383
  22. CHAPTER 14. Selected topics in the Morse-Novikov theory 413
  23. Backmatter 435
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