06-1350/Class Notes for Tuesday September 19

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Quick Plan

  • 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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  • 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?

Scanned Notes

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