The conjecture that Vassiliev invariants distinguish prime unoriented knots

A Vassiliev invariant is a finite-type invariant of knots; a knot is prime if it cannot be expressed as a nontrivial connected sum, and unoriented knots are considered without a choice of orientation. Vassiliev invariants distinguish all prime, unoriented knots. This was one of the optimistic conjectures about the nature of Vassiliev invariants discussed in the paper; the supplied source gives no resolution status.

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Primary source

Greg Kuperberg, “Detecting knot invertibility”, arXiv:q-alg/9712048 (1997).

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