函子纽结理论:纠纷、连贯、无条件变形和拓扑不变式的分类FUNCTORIAL KNOT THEORY
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分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者: 本社 编
出 版 社: Penguin
出版时间: 2001-12-1字数:版次:页数: 230印刷时间:开本:印次:纸张: 胶版纸I S B N : 9789810244439包装: 精装内容简介
Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory.
This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low- dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber's deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations.
目录
Acknowledgements
1. Introduction
I.Knots and Categories
2. Basic Concepts
2.1 Knots
2.2 Categories
3. Monoidal Categories, Functors and Natural Transformations
4. A Digression on Algebras
5. More About Monoidal Categories
6. Knot Polynomials
7. Categories of Tangles
8. Smooth Tangles and PL Tangles
9. Shum's Theorem
10. A Little Enriched Category Theory
II.Deformations
11. Introduction
12. Definitions
13. Deformation Complexes of Semigroupal Categories and Functors
14. Some Useful Cochain Maps
15. First Order Deformations
16. Obstructions and Cup Product and Pre-Lie Structures
17. Units
18. Extrinsic Deformations of Monoidal Categories
19. Vassiliev Invariants, Framed and Unframed
20. Vassiliev Theory in Characteristic 2
21. Categorical Deformations as Proper Generalizations of Classical Notions
22. Open Questions
22.1 Functorial Knot Theory
22.2 Deformation Theory
Bibliography
Index