http://www.artofproblemsolving.com/Forum/blog.php?u=55354&b=32193 (I posted these as my questions to a girl)
Today I asked my TA for the knot theory class whether there exists any analogs for Vassilev invariants, like at least in (2,4) case(to me the question is how to define singularities properly?). Also I asked him whether there exists any basic classifications(I guess we still use something like triangular moves). He told me to ask the professor, but the professor is not accessible, so I ask in here. I know the question seemed primitive(definitely not a research type question), I just don't know where I can find the needed reference.
Another question I want to ask is whether there exists any good integral type invariants. I feel it is highly unlikely to find one, but I don't know why. I think one criterion such an integral has to satisfy is it can distinguish small knotted parts in comparison with unknot parts, and it should be able to distinguish images with its mirror images.
