Talk:HOMFLY polynomial

[Untitled]

Apparently, the story is that Prztycki and Traczyk submitted their result but the initial manuscript got lost. Hence the -PT was belatedly appended. Mct mht 23:42, 4 April 2006 (UTC)

Chern-Simons theory

the connection with Chern-Simons theory should be incorporated. LeYaYa 22:49, 4 December 2006 (UTC)

References

I've added some and removed the unref tag. Richard Pinch (talk) 21:00, 11 June 2008 (UTC)

Confusing parts

I find parts of the article confusing:

1. What is a "split union of two links"? The two links with no crossings between them? We should make that clear.
2. The HOMFLY polynomial is initially defined in terms of variables m and l, but then the article seems to switch to alpha and z. Why not keep the notation consistent?
3. What are x, y, z in the third skein relation?
4. What is the meaning of # in $P(L_{1}\#L_{2})=P(L_{1})P(L_{2})\,$?

Help would be appreciated.--agr (talk) 15:00, 29 April 2009 (UTC)

1. Yes, a split union is the link obtained by taking a link diagram composed of disjoint link diagrams of the two links.
2. There are several parametrizations in the literature. Everyone has their own reason for using their convention, but it is simplest for this article to stick with one (I prefer the m and l version for perhaps no good reason except I included it to start the article).
3. This is the most general form of the HOMFLY relation. In the end, it's really the same invariant. But this relation looks nicer because it emphasizes the importance of the linear relation. From certain viewpoints, e.g. Witten's work relating quantum field theory to the HOMFLY polynomial., this is completely natural.
4. "#" refers to the sum of knots

--C S (talk) 21:05, 1 June 2009 (UTC)

Missing Pictures

Lots of pictures seem to be missing from this page --- or is it just me? I see error messages like this:

   Failed to parse (Cannot write to or create math output directory): P( \mathrm{unknot} ) = 1,\,

   Failed to parse (Cannot write to or create math output directory): \ell P(L_+) + \ell^{-1}P(L_-) + mP(L_0)=0,\,

I don't know how to fix this.

John Baez (talk) 20:17, 1 June 2009 (UTC)

It's just you.  :-) Or more accurately, last few months, Wikipedia servers have been a bit buggy for some reason (I haven't kept up with why). But the bugs go away after a bit. So I'd just try it again later. (Seems fine to me right now). --C S (talk) 20:27, 1 June 2009 (UTC)

Historical and Sociological Aspects

The article is purely mathematical. One of the interesting things about the HOMFLY polynomial is the history of the joint research announcement by four independent groups of researchers (the Cold War was still on, so Prztycki and Traczyk's fifth independent discovery was realized late). At the time the oddity of lack of quarreling over priority, common in other sciences, was so notable that the New York Times Science Times interviewed a lot of the principals. Of course, as one of them, I'm not the one to write such an addition for neutrality reasons, but someone might hunt up a link to the Science Times piece if it exists in the NYTimes archive and add a sentence with a link to the article.

Yetterdn (talk) 22:29, 25 November 2013 (UTC)

The only NY Times article I found was this: http://www.nytimes.com/1986/07/08/science/math-advance-penetrates-secrets-of-knots.html?pagewanted=all Do you know if there was another?--agr (talk) 01:41, 26 November 2013 (UTC)

That's the one, though the curiosity of four independent groups publishing together didn't seem to have made the editorial cut. Again, as one of the principals, my contribution to the article should be minimal, but you (or someone else) might want to add the link to that NYTimes article to the article. Yetterdn (talk) 18:46, 25 February 2014 (UTC)