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20Kb

The main difference between "real" and "mathematical" knots (or links) is that the first are open-ended, and the others are closed [1]. A mathematical knot is a homeomorphic image of a circle, and a link is a homeomorphic image of several circles. Two knots (or links) are equal iff their complements are homeomorphic. Otherwise, they are equal iff one could be obtained from the other by an ambient isotropy: a finite sequence of Redemeister moves [1, 9, 10, 13, 16, 19, 35, 49, 50].



9Kb         17Kb         18Kb

Redemeister moves I, II, III [1, 9, 10, 13, 16, 19, 35, 49, 50].