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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