06-1350/Class Notes for Tuesday September 19: Difference between revisions

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* Talk about some interesting properties of knots:
* Talk about some interesting properties of knots:
*# Can it be unknotted in less than 3 crossing changes?
*# Can it be unknotted in less than 3 crossing changes?
*# Does is bound a Seifert surface of genus less than 7? (See the program [http://www.win.tue.nl/~vanwijk/seifertview/ SeifertView] by [http://www.win.tue.nl/~vanwijk/ Jack van Wijk]).
⚫
*# Does it bound a disk in the 4-ball?
*# Is it a boundary link? (See an amusing list at the bottom of the Knot Atlas page on [http://katlas.math.toronto.edu/wiki/The_Multivariable_Alexander_Polynomial The Multivariable Alexander Polynomial]).
*# Is it fibered? (See an [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html animation] by Robert Barrington Leigh).
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*# Is it a ribbon knot? Does it bound a disk in the 4-ball?
{| align=center
|- valign=top
|[[Image:AKTLogo.png|thumb|300px|Our class logo]]
|[[Image:ClaspAndRibbonSingularities.png|thumb|140px|Forbidden and allowed]]
|}


* Briefly mention a few other interesting properties of knots:
* Briefly mention a few other interesting properties of knots:
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*# Does it have an alternating projection?
*# Does it have an alternating projection?
*# Is it algebraic?
*# Is it algebraic?
*# Does it have some symmetries?

Revision as of 19:28, 18 September 2006

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# 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 (), 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
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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?
Our class logo
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?
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