Ambient isotopy

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An ambient isotopy is the continuous deformation of a knot or link. This means the aspect of topology, where a knot or link may be bent, twisted, stretched, or pulled, as long as it is not allowed to intersect with itself or be cut.

Kurt Reidemeister proved that ambient isotopy can be described with only three moves, known as Reidemeister moves. An ambient isotopy that does not use the first Reidemeister move (meaning the knot or link is not twisted), then it is called Regular isotopy.