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: