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The number of Reidemeister moves for splitting a link

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Abstract.

We give an explicit upper bound for the number of Reidemeister moves for deforming a link diagram of a split link to be disconnected.

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References

  1. Birman, J.S., Menasco, W.W.: Studying links via closed braids. IV. Composite links and split links. Invent. Math. 102, 115–139 (1990)

    Google Scholar 

  2. Doll, H.: A generalized bridge number for links in 3-manifolds. Math. Ann. 294, 701–717 (1992)

    Google Scholar 

  3. Gordon, C. McA.: The theory of normal surface. Lecture notes typset by Richard P. Kent IV.

  4. Haken, W.: Theorie der Normalflächen. (German) Acta Math. 105, 245–375 (1961)

    Google Scholar 

  5. Haken, W.: Some results on surfaces in 3-manifolds. Studies in Modern Topology, Math. Assoc. Amer., 1968, pp.39–98.

  6. Hass, J., Lagarias, J.: The number of Reidemeister moves needed for unknotting. J. Amer. Math. Soc. 14, 399–428 (2001)

    Article  Google Scholar 

  7. Hayashi, C., Shimokawa, K.: Heegaard splittings of the trivial knot. J. Knot Theory Ramifications 7, 1073–1085 (1998)

    Article  Google Scholar 

  8. Kneser, H.: Geschlossene Flachen in dreidimensionalen Manigfaltigkeiten. Jahrresbericht der Deut. Math. Verein. 38, 248–260 (1929)

    Google Scholar 

  9. Trace, B.: On the Reidemeister moves of a classical knot. Proc. Amer. Math. Soc. 89, 722–724 (1983)

    Google Scholar 

  10. Vogel, P.: Representation of links by braids: a new algorithm. Comment. Math. Helv. 65, 104–113 (1990)

    Google Scholar 

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Correspondence to Chuichiro Hayashi.

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Mathematics Subject Classification (2000): 57M25, 57N10

The author is partially supported by Grant-in-Aid for Scientific Research (No. 15740047), Ministry of Education, Science, Sports and Technology, Japan.

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Hayashi, C. The number of Reidemeister moves for splitting a link. Math. Ann. 332, 239–252 (2005). https://doi.org/10.1007/s00208-004-0599-x

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  • DOI: https://doi.org/10.1007/s00208-004-0599-x

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