Timeline for Are homological knot invariants of finite type?
Current License: CC BY-SA 2.5
12 events
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| Sep 19, 2010 at 14:48 | comment | added | Charlie Frohman | I would echo ilya's answer/remark to the question as stated. However, as khovanov homology satisfies a skein long exact sequence, maybe there is a notion of finite type homological invariant, for which the statement could be true. | |
| Sep 19, 2010 at 0:06 | comment | added | Vivek Shende | @ Charlie: Yes. | |
| Sep 18, 2010 at 13:33 | comment | added | Charlie Frohman | I guess I need some disambiguation. What does the inquisitor mean by the "generating polynomials" of knot homology theories. Is this just the Poincare polynomial, with a variable for each grading? | |
| Sep 18, 2010 at 4:25 | answer | added | Ilya Kofman | timeline score: 4 | |
| Sep 13, 2010 at 21:49 | comment | added | Ben Webster♦ | Well, I don't think that finite type invariants detecting the unknot would be surprising, though that is a good argument that someone probably would have done it if it was easy. | |
| Sep 13, 2010 at 20:46 | comment | added | Noah Snyder | I was expecting the answer to be no, because otherwise you could show that finite type invariants distinguish the unknot by using facts about Heegaar-Floer homology. | |
| Sep 13, 2010 at 19:10 | comment | added | Ben Webster♦ | I suspect this is not known one way or the other. I don't think it's out of the question that the same ridiculously easy proof that works in the decategorified case (the R-matrix is congruent to its inverse mod h) works in cases like Khovanov-Rozansky, but I would have to think through the details before being sure. | |
| Sep 13, 2010 at 18:57 | comment | added | algori | Vivek -- excellent question! Although I think the relationship between finite type invariants and the generating functions for Khovanov homology may be trickier than just making a change of variables and taking the Taylor series. | |
| Sep 13, 2010 at 18:51 | history | edited | algori |
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| Sep 13, 2010 at 17:12 | comment | added | Vivek Shende | @Kevin: As far as I can tell, that paper says something like "categorified Jones invariants can be recovered from categorified finite type invariants". The question I was asking is: are the categorified Jones (and other quantum) invariants recoverable from the non-categorified finite type invariants. | |
| Sep 13, 2010 at 16:59 | comment | added | Kevin H. Lin | This is perhaps relevant: arXiv.org/abs/0803.1200 | |
| Sep 13, 2010 at 16:08 | history | asked | Vivek Shende | CC BY-SA 2.5 |