Vassiliev knot invariants

Chmutov S, Duzhin S and Mostovoy J (2010)), Introduction to Vassiliev Knot Invariants 1st Draft, http //www.math.osu.edu/ chmutov/preprints/. 

These measures are inspired by Vassiliev knot invariants.They form a natural progression of curve descriptors, much as moments of inertia and their correlations define solids. 

In summary, failure to detect a rigidly achiral presentation does not mean that such a presentation cannot be found among the infinitely many presentations of a knot failure to interconvert enantiomorphous presentations by ambient isotopy does not exclude the possibility that an interconversion pathway can be found among the infinitely many pathways that are available and a palindromic knot polynomial does not necessarily mean that the knot is amphicheiral. Consequently, it may be impossible in certain cases to determine with complete certainty whether a knot is topologically chiral or not. The fundamental task of the theory of knots was stated over a hundred years ago by its foremost pioneer Given the number of its double points, to find all the essentially different forms which a closed curve can assume. 15 Yet to find invariants that will definitively determine whether or not a knot is chiral remains an unsolved problem to this day.63a Vassiliev invariants have been conjectured to be such perfect invariants.63b... 

Deruchi, T., Tsurusaki, K., 1994. A statistical study of random knotting using the Vassiliev invariants. J. Knot Theory and Its Ramifications 3 321-353. 

---