Contents

Chapters in this book

1. Frontmatter I
2. Preface VII
3. Contents IX
4. Introduction 1
5. Part I. Towards Topological Field Theory
6. Chapter I. Invariants of graphs in Euclidean 3-space 17
7. Chapter II. Invariants of closed 3-manifolds 72
8. Chapter III. Foundations of topological quantum field theory 118
9. Chapter IV. Three-dimensional topological quantum field theory 152
10. Chapter V. Two-dimensional modular functors 236
11. Part II. The Shadow World
12. Chapter VI. 6j-symbols 301
13. Chapter VII. Simplicial state sums on 3-manifolds 345
14. Chapter VIII. Generalities on shadows 367
15. Chapter IX. Shadows of manifolds 394
16. Chapter X. State sums on shadows 435
17. Part III. Towards Modular Categories
18. Chapter XI. An algebraic construction of modular categories 493
19. Chapter XII. A geometric construction of modular categories 518
20. Appendix I. Dimension and trace re-examined 561
21. Appendix II. Vertex models on link diagrams 563
22. Appendix III. Gluing re-examined 565
23. Appendix IV. The signature of closed 4-manifolds from a state sum 568
24. References 571
25. Subject index 593