Warm-Up 10, Due Thursday, April 8, before class.

Please answer each question in three or more sentences. It is OK to answer 'I don't know' - but try and state why you are confused! No late Warm Ups are accepted for any reason, and only those submitted electronically through this web page (or by email, if the web page has technical problems) are considered.

Your Name:

Question 1

Is the knot below 5-colorable? Can the partial coloring (assigning values, colors, of 1 and 2 to two strands) be extended into a valid 5-coloring of all strands? What numbers do x and y then have to be?

Question 2

a) Why does a knot given by an non-reduced alternating projection always has also a projection with fewer crossing points?
b) Why does Kauffman, Murasugi, Thistlethwaite's Theorem imply that the two knots below are different (can not be transformed into each other)?

Question 3

Briefly explain any of the three paradoxes given in 7.1 in your own words.