06-1350/Class Notes for Tuesday September 19

06-1350/Navigation Panel   # Week of... Links 1 Sep 11 About, Tue, Thu 2 Sep 18 Tue, Kurlin(P), Thu 3 Sep 25 Tue, Photo, Thu 4 Oct 2 HW1, Tue, Thu 5 Oct 9 Tue(P), Thu(P) 6 Oct 16 HW2, Tue(P), Thu(P) 7 Oct 23 Tue(P), Thu 8 Oct 30 HW3, Tue, Thu 9 Nov 6 Tue ($\nu$), Thu 10 Nov 13 Tue, Thu 11 Nov 20 HW4(P), Thu 12 Nov 27 Thu 13 Dec 4 Syzygies in Asymptote, Final Jan 8 Grades Note. (P) means "contains a problem that Dror cares about". Add your name / see who's in! On to 07-1352

Quick Plan

• Talk about 06-1350/Some Equations by Kurlin.

• Talk about some interesting properties of knots:
  1. Can it be unknotted in less than 3 crossing changes?
  2. Does is bound a Seifert surface of genus less than 7? (See the program SeifertView by Jack van Wijk).
  3. Is it a boundary link? (See an amusing list at the bottom of the Knot Atlas page on The Multivariable Alexander Polynomial).
  4. Is it fibered? (See an animation by Robert Barrington Leigh).
  5. Is it a ribbon knot? Does it bound a disk in the 4-ball?

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Forbidden and allowed

• Briefly mention a few other interesting properties of knots:
  1. Is it the closure of a braid on at most 6 strands?
  2. Does it have a projection with less than 23 crossings?
  3. Does it have an alternating projection?
  4. Is it algebraic?
  5. Does it have some symmetries?