equivalence moves

In the 1930s, Reidemeister first rigorously proved that knots exist which are distinct from the unknot. He did this by showing that all knot deformations can be reduced to a sequence of three types of "moves, " called the (I) twist move, (II) poke move, and (III) slide move. These moves are most commonly called Reidemeister moves, although the term "equivalence moves" is sometimes also used. Reidemeister's theorem guarantees that moves I, II, and III correspond to ambient isotopy (moves II and III alone correspond to regular isotopy). He then defined the concept of colorability, which is invariant under Reidemeister moves.

ambient isotopy | knot move | Markov moves | regular isotopy | three-colorable knot | unknot | writhe