## S.V.Duzhin

### Vassiliev invariants and combinatorial structures

#### Lectures delivered at Graduate School of Mathematical Sciences

University of Tokyo

April--July 1999

**Remark**: these lecture notes are superceded by a new extended text
"CDBooK. Introduction to Vassiliev Knot Invariants", joint with
S.Chmutov. Draft version is available at my page in Russia
and Chmutov's page in
the US.
Contents of the course:

- Lecture 1. Definition of Vassiliev invariants.
- Lecture 2. Four term relation.
- Lecture 3. Bialgebra of chord diagrams.
- Lecture 4. Primitive elements. Intersection graphs.
- Lecture 5. Bialgebra of Feynman diagrams.
- Lecture 6. Bialgebra of Chinese characters.
- Lecture 7. The Kontsevich integral.
- Lecture 8. Properties of the Kontsevich integral.
- Lecture 9. The universal Vassiliev invariant.
- Lecture 10. Lie algebra weight systems.
- Lecture 11. The algebra of 3-graphs.
- Lecture 12. Vogel's algebra Lambda.
- Lecture 13. Algebra of arrow diagrams.
- Lecture 14. Upper and lower bounds for the number of Vassiliev
knot invariants.

The following materials are available on-line:

S.V.Duzhin