||Date of Monday
||Basic definitions. Isotopy. Isotopy invariants.
||Make knots out of old shoelaces, sticks,
(as seen in class!)
||Coloring. Checkerboards. Martix of coloring equations
and the determinant.
||Determinants. The coloring group. Examples.
||The coloring group is the first homology of the branched
double cover [Introduction to Knot Theory, Crowell and Fox].
||Mirrors. Inversions. Codes. Alexander polynomials.
||Hoste, Thistlethwaite, and Weeks use DT codes to find the
||Alexander polynomials and connect sums. Bridge position. Plats.
||Bridge presentation can be exponentially more complicated than
||Flypes. Braids (generators and relations) and their closures. Seifert circles.
||A braid applet by
||Every knot is isotopic to a braid closure.
Kauffman states. Kauffman polynomial.
||Kauffman's webpage. Alexander's
the Alexander polynomial.
||Jones polynomial. Span and crossing number.
||An on-line calculator
for the Jones polynomial.
from a lecture by John Conway. (He uses a different sign
convention from Sanderson's.) Conway's ZIP proof, by
Francis and Weeks.
||Knot genus and the Alexander polynomial. Conway, HOMFLY
polynomials. Relative strength of invariants. Video.
||Stills from the Not
Knot video. Lots of knots,
collected by Bar-Natan.