Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel

Chapters in this book

1. Frontmatter i
2. Contents v
3. Introduction 1
4. Chapter 1. Elliptic Riemann-Roch-Grothendieck and flat vector bundles 11
5. Chapter 2. The hypoelliptic Laplacian on the cotangent bundle 25
6. Chapter 3. Hodge theory, the hypoelliptic Laplacian and its heat kernel 44
7. Chapter 4. Hypoelliptic Laplacians and odd Chern forms 62
8. Chapter 5. The limit as t → +∞ and b → 0 of the superconnection forms 98
9. Chapter 6. Hypoelliptic torsion and the hypoelliptic Ray-Singer metrics 113
10. Chapter 7. The hypoelliptic torsion forms of a vector bundle 131
11. Chapter 8. Hypoelliptic and elliptic torsions: a comparison formula 162
12. Chapter 9. A comparison formula for the Ray-Singer metrics 171
13. Chapter 10. The harmonic forms for b → 0 and the formal Hodge theorem 173
14. Chapter 11. A proof of equation (8.4.6) 182
15. Chapter 12. A proof of equation (8.4.8) 190
16. Chapter 13. A proof of equation (8.4.7) 194
17. Chapter 14. The integration by parts formula 214
18. Chapter 15. The hypoelliptic estimates 224
19. Chapter 16. Harmonic oscillator and the J₀ function 247
20. Chapter 17. The limit of A^'2_φb,±H as b → 0 264
21. Bibliography 353
22. Subject Index 359
23. Index of Notation 361