An Ambient Isotopy, also known as an isotopy, is a continuous deformation of a knot or link. This represents the "rubber-sheet geometry" aspect of topology, where the knot or link may be bent, twisted, stretched, or pulled. Under no circumstances, however, may the curve be allowed to intersect itself or be cut.
Any group knots or links are considered ambiently isotopic or isotopic if there exists an Ambient Isotopy between them. Such a group is called an isotopic class. All members of an isotopic class, called projections, are considered to be the same knot or link.
Kurt Reidemeister proved that an Ambient Isotopy may be described in only three types of moves. These moves became known as the Reidemeister Moves. An Ambient Isotopy that does not use the first of these moves is called a Regular Isotopy