Monday, April 27

divbyzero 27 Apr 2009 20:52

**Topics from today's class**:

- Mike Landis' presentation
- Dan Barnak's presentation
- Olivia Dewey's presentation

**Homework**:

- To turn in on Thursday:
- 6.22
- Amphicheirality—look up the HOMFLY polynomial of your pet knot (note: their "z" is our "m" and their "a" is our "l") and use this to determine whether your knot is amphicheiral (see exercise 6.26). Note you may take for granted that the HOMFLY polynomial can detect both amphicheiral and non-amphicheiral 7-crossing knots (I'll turn this back to you on Friday so you can add it to the wiki)

- Wiki—the finished wiki project is due at the time our scheduled final exam would end:
**Tuesday, May 5, 5:00**. Still to do:- Final cleanup (look at the talk page and fix all outstanding issues)
- Braid representation: you did this on a previous homework. Now transfer it to the wiki. Draw your knot as a closed braid (in the justification box). Give the corresponding braid representation (on the main screen, outside the justification box)
- Span of the bracket polynomial: add a new section for this under genus. In the justification box you may use the lemma on page 160—you do not have to give the longer justification that you did in the homework. (This document should be self contained, so in your justification don't refer to "the lemma on page 160." Write a complete justification.)
- Just like we did for the Jones polynomial, look up the Alexander polynomial and the HOMFLY polynomial in the knot table. Then add them to your wiki page.
- Amphicheirality—I'll turn this back to you on Friday so you can add it to the wiki

**Note**: if you add this new material (braids, span, Alexander polynomial, HOMFLY polynomial) to the wiki by Thursday, then I will be able to look it over and comment on it so that you can clean it up by the final due date.