Isotopy invariant

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In Knot theory, an isotopy invariant is any property of a knot or link that remains consistent regardless of any ambient isotopy. This means that an isotopy invariant refers to the properties of a knot or link that remain constant even after the knot or link is deformed, twisted, bent, or pulled, as long as the knot or link is not allowed to intersect with itself or be cut.

Tricolorability is an example of an isotopy invariant, because a knot remains either tricolorable or non-tricolorable no matter how one deforms it.

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