# Some Vassiliev Invariant Questions

1. The V.I. definition goes doublepoint=overpass-underpass (or was it the other way around? If it's 50:50, I score 0 always :-). Would it lead anywhere to define doublepoint=overpass+underpass? (Even if it's equivalent. As I wouldn't have to guess then :-) I ask because I hate arrows on knots.

2. Stoimenow tabulated values for the 3-degree V.I., but only for knots. Has someone this data also for links? (Until 6 crossings already would be useful.)

3. Is this logic correct? Suppose you have a V.I. vanishing on all knots with >=2 doublepoints. Consider a clasp consisting of 2 doublepoints. From the definition then S^2+S^(-2)-2*S^0 = 0, where S is the usual braid generator resp. S matrix, and thus you can deduct a skein equation from the degree of a V.I. (and the higher the degree, the more of them).

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retagged: general topology -> quantum topology. General topology means point-set topology: en.wikipedia.org/wiki/General_topology –  Daniel Moskovich May 31 '11 at 3:22