**Instructor:** Dror
Bar-Natan, drorbn@math.huji.ac.il,
02-658-4187.

**Classes:** Tuesdays 14:00-16:00 at Sprintzak 215.

**Office hours:** Sundays 14:00-15:00 in my office, Mathematics 309.

**Agenda:** To learn about finite type knot invariants, and
especially about their multiply-proven but not-sufficiently-well
understood *fundamental theorem*, whose different proofs relate to
almost everything in mathematics.

**Further resources:**

- Advertisement Poster (with some extra syllabus details).
- Pathologies - strange things happen in the continuous category.
- A very simple Mathematica program that can verify the
invariance of the Kauffman bracket and compute it on small knots:
- Mathematica Notebook (requires Mathematica or MathReader).
- PDF (requires Acrobat Reader or GhostView.

- A handout on "Some Dimensions of A":
- ChordDiagrams.pdf.
- The files needed to make ChordDiagrams.ps: ChordDiagrams.zip.

- Class notes for April 17th, 2001. (Reminders, the algebra structure of , algebras and co-algebras, the co-algebra structure of )
- Class notes for April 24th, 2001. (The co-algebra structure of , tensor products of representations of algebras and the notion of "a bialgebra", is a bialgebra, preview of the relation between , diagrams and Lie algebras).
- Class notes for May 1st, 2001. (Proof that STU is equivalent to 4T, Lie algebras, representations and weight systems).
- Class notes for May 22nd, 2001. (Universal invariants, cabling, knotted trivalent graphs and their finite type invariants, the basic operations).
- Class notes for May 29th, 2001. (Finite generation of knotted trivalent graphs, diagrammatic versions of knot-theoretic operations).
- Class notes for June 5th, 2001. (More on the diagrammatic versions of knot-theoretic operations, gauge transformations on universal invariants).
- Class notes for June 12th, 2001. (Universality, more on gauge transformations).
- Class notes for June 19th, 2001. (Getting rid of orientations, more on gauge transformations, the most general general invariance argument, identifying (graph) in simpler terms)
- Class notes for June 26th, 2001. (The Pachner move, linearization, beginning of symmetrization).
- If you're taking this class for credit, you must write a project.

**Class Photo, April 17, 2001**

Background image: A table of knots and links by Rob Scharein, taken from http://www.cs.ubc.ca/nest/imager/contributions/scharein/zoo/knotzoo.html.