Ukraine Canada Summer School 2006 Talk I: Difference between revisions

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Also see {{Home Link|classes/0102/FeynmanDiagrams/NonObvious/index.html|Some Non Obvious Examples}}.

===Questions===
===Questions===


* Is the [http://katlas.math.toronto.edu/wiki/3_1 trefoil knot] really knotted?
* Is the {{KAT Link|3_1|trefoil knot}} really knotted?
* Is the trefoil knot equivalent to its mirror image?
* Is the trefoil knot equivalent to its mirror image?
* Are [http://katlas.math.toronto.edu/wiki/K11n34 K11n34] (the "Conway" knot) and [http://katlas.math.toronto.edu/wiki/K11n42 K11n42] (the "Kinoshita-Terasaka" knot) really different?
* Are {{KAT Link|K11n34|K11n34}} (the "Conway" knot) and {{KAT Link|K11n42|K11n42}} (the "Kinoshita-Terasaka" knot) really different?
{| align=center
|-
|[[Image:K11n34.png]]
|[[Image:K11n42.png]]
|}
* Which of these two is the knot at the gate of the Cambridge University maths department?
* Which of these two is the knot at the gate of the Cambridge University maths department?
{| align=center
|-
|[[Image:Gateknot-negated.jpg|400px]]
|}
* Can you make a list of all knots?
* Can you make a list of all knots?
* The trefoil knot is bounds a Seifert surface. Do all knots do?
* The trefoil knot is bounds a Seifert surface. Do all knots do?
* The complement of the trefoil knot is "fibered" with Seifert surfaces (see [http://www.math.toronto.edu/~drorbn/People/BarringtonLeigh/FiberedKnot.html animation]). Is that true for all knots? How does one decide?
* The complement of the trefoil knot is "fibered" with Seifert surfaces (see {{Home Link|People/BarringtonLeigh/FiberedKnot.html|animation}}). Is that true for all knots? How does one decide?
* Which knots are boundary knots?
* Which knots are ribbon knots?
* Which knots are slice knots?
* Which knots are slice knots?
* And always, the hardest and most important question in mathematics: '''Why should we care??'''
* And always, the hardest and most important question in mathematics: '''Why should we care??'''

Latest revision as of 12:47, 5 December 2007

Also see Some Non Obvious Examples.

Questions

  • Is the trefoil knot really knotted?
  • Is the trefoil knot equivalent to its mirror image?
  • Are K11n34 (the "Conway" knot) and K11n42 (the "Kinoshita-Terasaka" knot) really different?
K11n34.png K11n42.png
  • Which of these two is the knot at the gate of the Cambridge University maths department?
Gateknot-negated.jpg
  • Can you make a list of all knots?
  • The trefoil knot is bounds a Seifert surface. Do all knots do?
  • The complement of the trefoil knot is "fibered" with Seifert surfaces (see animation). Is that true for all knots? How does one decide?
  • Which knots are ribbon knots?
  • Which knots are slice knots?
  • And always, the hardest and most important question in mathematics: Why should we care??

Some Answers

  • 3-colourings.
  • The Kauffman bracket and the Jones polynomial.
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