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Classical knot theory studies the position of a circle (knot) or of several circles (link) in R or S = R3∪∞. The fundamental problem of classical knot theory is the classification of links (including knots) up to the natural movement in space which is called an ambient isotopy. To distinguish knots or links we look for invariants of links, that is, properties of links which are unchanged under ambient isotopy. When we look for invariants of links we have to take into account the following three criteria:

3-coloring and other elementary invariants of knots