Introduction to Vassiliev knot invariants
By: S. Chmutov, S. Duzhin, J. Mostovoy
Contributors: Duzhin, S. V. (Sergeĭ Vasilʹevich), 1956-; Mostovoy, J. (Jacob)
Publisher: Cambridge University Press
Published: 2012
Place of publication: New York
Language: eng
ISBN-13: 9781107020832
Subjects: Invariants; Knot theory; MATHEMATICS / Topology
Description: "With hundreds of worked examples, exercises and illustrations, this detailed exposition of the theory of Vassiliev knot invariants opens the field to students with little or no knowledge in this area. It also serves as a guide to more advanced material. The book begins with a basic and informal introduction to knot theory, giving many examples of knot invariants before the class of Vassiliev invariants is introduced.This is followed by a detailed study of the algebras of Jacobi diagrams and 3-graphs, and the construction of functions on these algebras via Lie algebras. The authors then describe two constructions of a universal invariant with values in the algebra of Jacobi diagrams: via iterated integrals and via the Drinfeld associator, and extend the theory to framed knots"--
Table of contents: title: Machine generated contents note: 1. Knots and their relatives; 2. Knot invariants; 3. Finite type invariants; 4. Chord diagrams; 5. Jacobi diagrams; 6. Lie algebra weight systems; 7. Algebra of 3-graphs; 8. The Kontsevich integral; 9. Framed knots and cabling operations; 10. The Drinfeld associator; 11. The Kontsevich integral: advanced features; 12. Braids and string links; 13. Gauss diagrams; 14. Miscellany; 15. The space of all knots; Appendix; References; Notations; Index.