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Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants /
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 natural...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; River Edge, NJ :
World Scientific,
©2001.
|
| Colección: | K & E series on knots and everything ;
v. 26. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 049 | |a UAMI | ||
| 100 | 1 | |a Yetter, David N. | |
| 245 | 1 | 0 | |a Functorial knot theory : |b categories of tangles, coherence, categorical deformations, and topological invariants / |c David N. Yetter. |
| 246 | 3 | 0 | |a Categories of tangles, coherence, categorical deformations, and topological invariants |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c ©2001. | ||
| 300 | |a 1 online resource (230 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 490 | 1 | |a K & E series on knots and everything ; |v v. 26 | |
| 504 | |a Includes bibliographical references (pages 219-224) and index. | ||
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |a 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. | |
| 520 | |a 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. | ||
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Knot theory. | |
| 650 | 0 | |a Categories (Mathematics) | |
| 650 | 0 | |a Functor theory. | |
| 650 | 6 | |a Théorie des nœuds. | |
| 650 | 6 | |a Catégories (Mathématiques) | |
| 650 | 6 | |a Théorie des foncteurs. | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Categories (Mathematics) |2 fast | |
| 650 | 7 | |a Functor theory |2 fast | |
| 650 | 7 | |a Knot theory |2 fast | |
| 650 | 1 | 7 | |a Knopentheorie. |2 gtt |
| 650 | 7 | |a Topologia. |2 larpcal | |
| 776 | 0 | 8 | |i Print version: |a Yetter, David N. |t Functorial knot theory. |d Singapore ; River Edge, NJ : World Scientific, ©2001 |z 9810244436 |z 9789810244439 |w (DLC) 2001273934 |w (OCoLC)47684546 |
| 830 | 0 | |a K & E series on knots and everything ; |v v. 26. | |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=235892 |z Texto completo |
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