View source for Ukraine Canada Summer School 2006 Talk I

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

===Questions===

* Is the {{KAT Link|3_1|trefoil knot}} really knotted?
* Is the trefoil knot equivalent to its mirror image?
* Are {{KAT Link|K11n34|K11n34}} (the "Conway" knot) and {{KAT Link|K11n42|K11n42}} (the "Kinoshita-Terasaka" knot) really different?
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|[[Image:K11n34.png]]
|[[Image:K11n42.png]]
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* Which of these two is the knot at the gate of the Cambridge University maths department?
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|[[Image:Gateknot-negated.jpg|400px]]
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* 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 {{Home Link|People/BarringtonLeigh/FiberedKnot.html|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.