| 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. |
|
|
|
