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Functorial knot theory : categories of tangles, coherence, categorical deformations, and topological invariants / David N. Yetter.
Math/Physics/Astronomy Library QA612.2 .Y48 2001
Available
- 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:
- 230 pages : illustrations ; 23 cm.
- Other Title:
- Categories of tangles, coherence, categorical deformations, and topological invariants
- Place of Publication:
- Singapore ; River Edge, NJ : World Scientific, [2001]
- Summary:
- As part of a series exploring why knot theory serves as a nexus for math, physics, biology, and philosophy, this volume probes the quantum topology links between the pivotal objects of study in low- dimensional geometric topology--including classical knots--and such exotic algebraic objects as Hopf algebras and monoidal categories. Yetter (mathematics, Kansas State U.) covers basic concepts and categories, and provides proofs of some universally assumed "folk theorems," examples of knot diagrams, and 63 references. The section on deformations assumes some familiarity with algebraic deformation theory and homological algebra. c. Book News Inc.
- Contents:
- I Knots and Categories
- 2.1 Knots 14
- 2.2 Categories 26
- 3. Monoidal Categories, Functors and Natural Transformations 39
- 4. A Digression on Algebras 61
- 5. More About Monoidal Categories 71
- 6. Knot Polynomials 83
- 7. Categories of Tangles 87
- 8. Smooth Tangles and PL Tangles 97
- 9. Shum's Theorem 117
- 10. A Little Enriched Category Theory 131
- II Deformations
- 13. Deformation Complexes of Semigroupal Categories and Functors 149
- 14. Some Useful Cochain Maps 153
- 15. First Order Deformations 155
- 16. Obstructions and Cup Product and Pre-Lie Structures on X (F) 159
- 17. Units 175
- 18. Extrinsic Deformations of Monoidal Categories 181
- 19. Vassiliev Invariants, Framed and Unframed 185
- 20. Vassiliev Theory in Characteristic 2 201
- 21. Categorical Deformations as Proper Generalizations of Classical Notions 209
- 22. Open Questions 213
- 22.1 Functorial Knot Theory 213
- 22.2 Deformation Theory 214.
- Notes:
- Includes bibliographical references (pages 219-224) and index.
- ISBN:
- 9810244436
- OCLC:
- 47684546
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