Fall 2010 Knot Theory (unnumbered course)
Meeting time and place: Tuesdays 9:30-10:30, Room 105 (Seminar Room)
Textbooks:
Prasolov and Sossinsky, Knots, Links, Braids, and 3-Manifolds
Rolfsen, Knots and Links
Lickorish, An Introduction to Knot Theory
Tentative Schedule:
| Date |
Topic |
Presenter |
Notes |
|
September 15
|
intro/basics
|
Diana
|
|
September 21
|
braids
|
Joris
|
|
September 28
|
Seifert surfaces
|
Ian
|
Seifert Surfaces
|
|
October 5
|
classical invariants: genus, unknotting #, crossing #, (bridge #?), torus knots
|
Dale
|
|
October 12
|
Alexander-Conway polynomial, skein relations
|
Diana
|
|
October 19
|
Alexander module, linking #, Seifert matrix
|
Robin
|
see Rolfsen 7A,B, example 6B1; 5D; 8A,C.
|
|
October 26
|
more on the Alexander module
|
Robin
|
More Alexander (see also Rolfsen 7B, 8C)
|
|
November 2
|
-
|
-
|
|
November 9
|
Vassiliev (finite-type) invariants
|
Robin
|
Vassiliev
|
|
November 16
|
Jones polynomial
|
Dale
|
|
November 23
|
knot theory and number theory
|
Ian
|
Knots and Numbers
|
|
November 30
|
-
|
-
|
|
December 7
|
Khovanov homology
|
Danny
|
|
December 14
|
3-manifolds via surgery on S^3
|
Joris
|
|