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Knot invariant

This term is related to: knot theory

Definition

A knot invariant is a function from the set of all knots (embeddings of S^1 in S^3) to some set, which is invariant under isotopy; in other words, if there is a self-homeomorphism of S^3, isotopic to the identity map, which sends one knot to the other, then the function should take the same value on both knots.

Note that isotopy-invariance is a weaker condition than being invariant under self-homeomorphisms, because the sphere possesses an orientation-reversing self-homeomorphism.

A list of knot invariants can be found at:

Category:Knot invariants