# Ukraine Canada Summer School 2006 Talk I

From Drorbn

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.