It is not known at present whether the Kontsevich integral, or the totality of Vassiliev invariants, is a complete knot invariant. Computation of the Kontsevich integral, which has values in an algebra of chord diagrams, turns out to be rather difficult and has been done only for a few classes of knots up to now. There is no finite-type invariant of degree less than 11 which distinguishes mutant knots. See also Willerton's fish References Further reading Victor A. Vassiliev, Cohomology of knot spaces. Theory of singularities and its applications, 23–69, Adv. Soviet Math., 1, American Mathematical Society, Providence, RI, 1990. Joan Birman and Xiao-Song Lin, Knot polynomials and Vassiliev's invariants.'' Inventiones Mathematicae, 111, 225–270 (1993) External links Knot invariants 3-manifolds