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Mathematical Notes

, Volume 105, Issue 1–2, pp 115–122 | Cite as

Classification of Unknotted Ribbons in the Plane and on the Sphere

Article

Abstract

The aim of this paper is to classify unknotted ribbons in the plane and on the sphere up to regular isotopy.

Keywords

regular isotopy knot diagram Reidemeister moves 

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References

  1. 1.
    L. H. Kauffman, “An Invariant of Regular Isotopy,” Trans. Amer. Math. Soc. 318, 417–471 (1990).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    S. Matveev, “Straightening Contours on the Plane,” Kvant 4, 22–28 (1983).Google Scholar
  3. 3.
    B. Trace, “On the ReidemeisterMoves of a Classical Knot,” Proc. Amer. Math. Soc. 89 (4), 722–724 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    O. Ostlund, “Invariants of Knot Diagrams and Relations among ReidemeisterMoves,” Journal of Knot Theory and Its Ramifications 10 (8), 1215–1227 (2001).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Bryn Mawr CollegeBryn MawrUSA

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