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}}. |
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===Questions=== |
===Questions=== |
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* Is the |
* Is the {{KAT Link|3_1|trefoil knot}} really knotted? |
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* Is the trefoil knot equivalent to its mirror image? |
* Is the trefoil knot equivalent to its mirror image? |
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* Are |
* Are {{KAT Link|K11n34|K11n34}} (the "Conway" knot) and {{KAT Link|K11n42|K11n42}} (the "Kinoshita-Terasaka" knot) really different? |
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* 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? |
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* Can you make a list of all knots? |
* Can you make a list of all knots? |
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* The trefoil knot is bounds a Seifert surface. Do all knots do? |
* The trefoil knot is bounds a Seifert surface. Do all knots do? |
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* The complement of the trefoil knot is "fibered" with Seifert surfaces (see |
* 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? |
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* Which knots are |
* Which knots are ribbon knots? |
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* Which knots are slice knots? |
* Which knots are slice knots? |
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* 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?
![]() |
![]() |
- Which of these two is the knot at the gate of the Cambridge University maths department?
![]() |
- 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.