S. Chmutov

Introduction to Vassiliev Knot Invariants (eBook, PDF)

• Format: PDF

Produktbeschreibung

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. Various other topics are then discussed, such as Gauss diagram formulae, before the book ends with Vassiliev's original construction.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. Mai 2012
• Englisch
• ISBN-13: 9781139415811
• Artikelnr.: 38276493

Autorenporträt

S. Chmutov is Associate Professor in the Department of Mathematics at Ohio State University.

Inhaltsangabe

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.