| Description |
1 online resource (230 pages) : illustrations. |
| Physical Medium |
polychrome |
| Description |
text file |
| Series |
K & E series on knots and everything ; v. 26
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K & E series on knots and everything ; v. 26.
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| Bibliography |
Includes bibliographical references (pages 219-224) and index. |
| Contents |
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 on X[symbol](F) -- 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. |
| Summary |
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. |
| Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
| Subject |
Knot theory.
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Knot theory. |
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Categories (Mathematics)
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Categories (Mathematics) |
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Functor theory.
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Functor theory. |
| Genre/Form |
Electronic books.
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Electronic books.
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| Added Title |
Categories of tangles, coherence, categorical deformations, and topological invariants |
| Other Form: |
Print version: Yetter, David N. Functorial knot theory. Singapore ; River Edge, NJ : World Scientific, ©2001 9810244436 9789810244439 (DLC) 2001273934 (OCoLC)47684546 |
| ISBN |
9789812810465 (electronic book) |
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9812810463 (electronic book) |
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9789810244439 |
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9810244436 |
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