Ukraine Canada Summer School 2006 Talk I: Difference between revisions
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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 [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 [http://www.math.toronto.edu/~drorbn/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??''' |
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Revision as of 12:48, 15 August 2006
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?
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- 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?
- 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.
