Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants /

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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...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Yetter, David N.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Singapore ; River Edge, NJ : World Scientific, ©2001.
Colección:K & E series on knots and everything ; v. 26.
Temas:
Knot theory.
Categories (Mathematics)
Functor theory.
Théorie des nœuds.
Catégories (Mathématiques)
Théorie des foncteurs.
MATHEMATICS > Topology.
Functor theory
Knot theory
Knopentheorie.
Topologia.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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