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