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.

Author: S. Chmutov, S. Duzhin, J. Mostovoy
Binding Type: Hardcover
Publisher: Cambridge University Press
Published: 07/09/2012
Pages: 520
Weight: 2.4lbs
Size: 9.80h x 6.90w x 1.30d
ISBN: 9781107020832


Review Citation(s):
Choice 02/01/2013

About the Author
Chmutov, S.: - S. Chmutov is Associate Professor in the Department of Mathematics at Ohio State University.Duzhin, S.: - S. Duzhin is a Senior Researcher in the St Petersburg Department of the Steklov Institute of Mathematics.Mostovoy, J.: - J. Mostovoy is Professor in the Department of Mathematics at the Centre for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV-IPN), Mexico City.