Algebraic & Geometric Topology

Ordering the Reidemeister moves of a classical knot

Alexander Coward

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Abstract

We show that any two diagrams of the same knot or link are connected by a sequence of Reidemeister moves which are sorted by type.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 2 (2006), 659-671.

Dates
Received: 8 June 2005
Revised: 13 April 2006
Accepted: 17 April 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796540

Digital Object Identifier
doi:10.2140/agt.2006.6.659

Mathematical Reviews number (MathSciNet)
MR2240911

Zentralblatt MATH identifier
1095.57005

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
knot diagram Reidemeister move

Citation

Coward, Alexander. Ordering the Reidemeister moves of a classical knot. Algebr. Geom. Topol. 6 (2006), no. 2, 659--671. doi:10.2140/agt.2006.6.659. https://projecteuclid.org/euclid.agt/1513796540


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References

  • J Hass, J C Lagarias, The number of Reidemeister moves needed for unknotting, J. Amer. Math. Soc. 14 (2001) 399–428
  • K Reidemeister, Knotten und Gruppen, Abh. Math. Sem. Univ. Hamburg 5 (1927) 7–23
  • B Trace, On the Reidemeister moves of a classical knot, Proc. Amer. Math. Soc. 89 (1983) 722–724