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Knot theory is dealing with embedding of curves in manifolds of dimension 3. A knot is a single circle embedded in the affine space of dimension 3 as a smooth curve not crossing itself. Many knot invariants are known and can be used to distinguish knots.

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Kontsevich integral : state of the art

The Kontsevich integral is known to be a universal Vassiliev invariant. It is still an open question whether it is a complete knot invariant, i.e. whether it distinguishes a given knot from all other …