zbMATH — the first resource for mathematics

Ordering the Reidemeister moves of a classical knot. (English) Zbl 1095.57005
This paper refines Reidemeister’s classical theorem to show that if two diagrams represent the same link then there is a sequence of Reidemeister moves connecting them in which increasing moves of type I and then type II are done first, followed by type III moves and finally decreasing moves of type II and then type I. Type I moves can be omitted if corresponding components all have the same writhe and winding number. The proof is combinatorially based, using some preliminary lemmas to permit the inductive modification of an original minimal sequence of unsorted moves between the diagrams.

57M25 Knots and links in the \(3\)-sphere (MSC2010)
57M27 Invariants of knots and \(3\)-manifolds (MSC2010)
Full Text: DOI EMIS arXiv
[1] J Hass, J C Lagarias, The number of Reidemeister moves needed for unknotting, J. Amer. Math. Soc. 14 (2001) 399 · Zbl 0964.57005
[2] K Reidemeister, Knotten und Gruppen, Abh. Math. Sem. Univ. Hamburg 5 (1927) 7
[3] B Trace, On the Reidemeister moves of a classical knot, Proc. Amer. Math. Soc. 89 (1983) 722 · Zbl 0554.57003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.