Introduction to Vassiliev knot invariants
 Responsibility
 S. Chmutov, S. Duzhin, J. Mostovoy.
 Language
 English.
 Imprint
 Cambridge, UK ; New York : Cambridge University Press, 2012.
 Physical description
 xvi, 504 p. : ill ; 26 cm.
Access
Available online
 dx.doi.org Cambridge Books Online Access limited to one user.
Math & Statistics Library

Stacks

Unknown
QA612.2 .C48 2012

Unknown
QA612.2 .C48 2012
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Creators/Contributors
 Author/Creator
 Chmutov, S. (Sergei), 1959
 Contributor
 Duzhin, S. V. (Sergeĭ Vasilʹevich), 1956
 Mostovoy, J. (Jacob)
Contents/Summary
 Bibliography
 Includes bibliographical references (p. [483]495) and index.
 Contents

 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 3graphs 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.
 (source: Nielsen Book Data)
 Publisher's Summary
 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 3graphs, 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.
(source: Nielsen Book Data)  Supplemental links
 Cover image
Subjects
 Subject
 Knot theory.
 Invariants.
Bibliographic information
 Publication date
 2012
 ISBN
 9781107020832 (hardback)
 1107020832 (hardback)