Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 30 ]]>

- 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.

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 27 ]]>

- Amphicheiral knots
- The bracket, X, and HOMFLY polynomials for amphicheiral knots

**Homework**:

- 6.22 (due next Thursday)
- Begin cleaning up your wiki—go to the talk page and make the changes mentioned there.

**Presentations**:

- Monday: Mike, Dan, Olivia
- Thursday: Richard, Tan, Topher, Erik

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 23 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

What is the "signature" invariant that Adams refers to on p. 178?

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

- Alexander polynomial
- HOMFLY polynomial

**Homework**:

- 6.14 (you may use the resolving tree method I showed you in class), 6.15, compute the HOMFLY polynomial for the figure eight knot (you may use the resolving tree method I showed you in class), 6.21

**Read for next class**:

- 6.4

**Announcements**:

- Email me if you have a preference of presenting on Monday versus Thursday next week (first come first served for time slots)

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 20 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

- Alternating projections and crossing number
- The Alexander polynomial
- resolving trees

**Homework**:

- Wiki:
- Fill in the section on the genus of your pet knot
- Look up the Jones polynomial for your knot in this knot table and add it to your wiki page. In your justification, simply link to the knot table.

**Read for next class**:

- 6.3

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 16 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 6 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 2 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 2 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 6 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 6 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

- Another look at the bracket polynomial
- The span of a polynomial
- The span the bracket polynomial for alternating knots

**Homework**:

- 6.9 (you don't have do the entire bracket polynomial, just compute the contribution from 4 different states), 6.10, 6.11
- Pet knot: compute the span of the bracket polynomial for your pet knot. Use the techniques that we saw in the proof of today's main lemma. You do not have to compute the bracket polynomial. You may not use the result of the lemma to answer this question (although it will give you a good check).
- Wiki (due next Monday):
- Fill in the section on the genus of your pet knot
- Look up the Jones polynomial for your knot in this knot table and add it to your wiki page. In your justification, simply link to the knot table.

**Read for next class**:

- 6.3

**Announcements**:

- Remember that a first draft of your paper is due on Thursday.

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 13 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

- The bracket polynomial
- Writhe
- The X polynomial
- The Jones polynomial

**Homework**:

- 6.3, 6.4, 6.5, 6.7, 6.8

**Read for next class**:

- 6.2

Forum category: Daily postings / Homework and discussions

Forum thread: Thursday, April 9 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 6 ]]>

Forum category: Daily postings / Homework and discussions

Forum thread: Monday, April 6 ]]>