Ukraine Canada Summer School 2006 Talk I: Difference between revisions
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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 [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 [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? |
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|[[Image:K11n34.png]] |
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|[[Image:K11n42.png]] |
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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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[[Image:Gateknot-negated.jpg|400px|center]] |
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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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Revision as of 11:43, 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?
- 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 boundary 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.
