Ukraine Canada Summer School 2006 Talk I

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.