I have a few questions around the 3move. I know it's NOT an unknotting
move (but who needs knots with 20+ crossings anyway :) by the recent proof
of Przytycki.
1. In another paper about the third skein module, he conjectures about
a knot polynomial based on a cubic skein equation. Is this polynomial
still conjectural (at last so I understood the paper)? (I'm not uptodate
with the literature, naturally.)
1a) Regardless whether yes or no, is this polynomial "meant" for directed links?
2. Instead of 3move, consider the skein equation
$S^2+a1*S^1+a2*S^0+a3*S^{1}+a0*H=0$
(where S is the S matrix and H the TemperleyLieb generator/the 0 tangle).
This is more or less equivalent to the 3move (e.g. I always "knew" the
Borromean double would spell trouble, which also was the timewise first
counterexample for MontesinoNakanishi). I say "more or less" because if
you eliminate H you are already in the fourth skein module. Also this
is for undirected links only. But I only want to know if the unknotting
power is the same, i.e. deleting clasps unknots exactly the same knots
as the 3move.
Take the 2minute tour
×
MathOverflow is a question and answer site for professional mathematicians. It's 100% free, no registration required.


