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.
- Advertisement Poster (with some extra
- 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:
- A handout on "Some Dimensions of A":
- 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
- Class notes for May 1st, 2001. (Proof that
STU is equivalent to 4T, Lie algebras, representations and weight
- 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
- 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
- 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
Click on the image to get the full size version
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.