An exposition of building blocks for deformation theory of braided monoidal categories, giving rise to sequences of Vasseliv invariants of framed links, clarifying the interrelations between them.
Author(s): David N. Yetter
Series: Series on Knots and Everything
Publisher: World Scientific Pub Co (
Year: 2001
Language: English
Pages: 238
Acknowledgements ......Page 8
Contents ......Page 10
1. Introduction ......Page 14
I Knots and Categories ......Page 18
2. Basic Concepts ......Page 20
3. Monoidal Categories Functors and Natural Transformations ......Page 46
4. A Digression on Algebras ......Page 68
5. More About Monoidal Categories ......Page 78
6. Knot Polynomials ......Page 90
7. Categories of Tangles ......Page 94
8. Smooth Tangles and PL Tangles ......Page 104
9. Shum's Theorem ......Page 124
10. A Little Enriched Category Theory ......Page 138
II Deformations ......Page 146
11. Introduction ......Page 148
12. Definitions ......Page 150
13. Deformation Complexes of Semigroupal Categories and Functors ......Page 156
14. Some Useful Cochain Maps ......Page 160
15. First Order Deformations ......Page 162
16. Obstructions and Cup Product and Pre-Lie Structures on X'(F) ......Page 166
17. Units ......Page 182
18. Extrinsic Deformations of Monoidal Categories ......Page 188
19. Vassiliev Invariants Framed and Unframed ......Page 192
20. Vassiliev Theory in Characteristic 2 ......Page 208
21. Categorical Deformations as Proper Generalizations of Classical Notions ......Page 216
22. Open Questions ......Page 220
Bibliography ......Page 226
Index ......Page 232
