MA3F2, Knot Theory
Winter 2008


Week Date of Monday Topics Example sheet Lecture notes Comments
1 Jan. 7 Basic definitions. Isotopy. Isotopy invariants. One One An on-line knot table.
2 Jan. 14 Coloring. Checkerboards. Martix of coloring equations and the determinant. Two Two
3 Jan. 21 Determinants. The coloring group. Examples. Three Three
4 Jan. 28 Mirrors. Inversions. Codes. Alexander polynomials. Four Four Fixed the statement of Exercise 4.3. Hoste, Thistlethwaite, and Weeks use DT codes to find the first 1,701,936 knots. (Takes half a minute to download.)
5 Feb. 4 Connect sums. Bridge position. Plats. None. None.
6 Feb. 11 Flypes. Braids (generators and relations). Every knot is isotopic to a braid closure. A braid applet by Stephen Bigelow.
7 Feb. 18 Kauffman states. Kauffman polynomial.
8 Feb. 25 Jones polynomial. An on-line calculator for the Jones polynomial.
9 Mar. 3 Span of the Jones polynomial. Tangles. Surfaces.
10 Mar. 10 Knot genus. Conway, HOMFLY polynomials. Video.