Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants / David N. Yetter.

Format:

Book

Author/Creator:

Yetter, David N.

Series:

K & E series on knots and everything ; vol. 26.

K & E series on knots and everything ; vol. 26

Language:

English

Subjects (All):

Knot theory.

Categories (Mathematics).

Functor theory.

Physical Description:

1 online resource (238 p.)

Edition:

1st ed.

Other Title:

Categories of tangles, coherence, categorical deformations, and topological invariants

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2001.

Language Note:

English

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 turn

Contents:

Contents ; Acknowledgements ; 1. Introduction ; I Knots and Categories ; 2. Basic Concepts ; 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'(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 ; Bibliography ; Index

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 219-224) and index.

ISBN:

9786611956165

9781281956163

1281956163

9789812810465

9812810463

OCLC:

879023764