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The determination of the pairs of two-bridge knots or links with Gordian distance one


Author: Ichiro Torisu
Journal: Proc. Amer. Math. Soc. 126 (1998), 1565-1571
MSC (1991): Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-98-04181-1
MathSciNet review: 1425140
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Abstract: We thoroughly determine the pairs of two-bridge knots or links with Gordian distance one. In addition, we examine the Gordian distance between a Montesinos knot (or link) and a two-bridge knot (or link).


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  • 1. Boyer, S. and Zhang, X., Exceptional surgery on knots, Bull. AMS (2) 31 (1994), 197-203. MR 95f:57035
  • 2. Burde, G. and Zieschang, H., Knots, de Gruyter Studies in Mathematics, no. 5, Walter de Gruyter, Berlin, 1985. MR 87b:57004
  • 3. Culler, M., Gordon, C.McA., Luecke, J. and Shalen, P., Dehn surgery on knots, Ann. of Math. (2) 125 (1987), 237-300. MR 88h:57026
  • 4. I. Dazey and D. W. Sumners, A strand passage metric for topoisomerase action, Proceedings of Knots 96 (ed. by S. Suzuki), World Scientific Publishing Co. (1997), 267-278.
  • 5. Gordon, C.McA., Dehn surgery and satellite knots, Trans. Amer. Math. Soc. 275 (1983), 687-708. MR 84d:57003
  • 6. Heil, W., 3-manifolds that are sums of solid tori and Seifert fiber spaces, Proc. Amer. Math. Soc. 37 (1973), 609-614. MR 50:8526
  • 7. Kanenobu, T. and Murakami, H., Two-bridge knots with unknotting number one, Proc. Amer. Math. Soc. 98 (1986), 499-502. MR 87i:57005
  • 8. Kohn, P., Two-bridge links with unlinking number one, Proc. Amer. Math. Soc. 113 (1991), 1135-1147. MR 92c:57008
  • 9. Lickorish, W.B.R., The unknotting number of a classical knot, Contemp. Math., vol. 44, Amer. Math. Soc., Providence, RI, 1985, pp. 117-121. MR 87a:57012
  • 10. Montesinos, J.M., Classical Tessellations and Three-Manifolds, Springer-Verlag, 1987. MR 89d:57016
  • 11. Montesinos, J.M, Surgery on links and double branched coverings of $S^{3}$, Ann. of Math. Studies 84 (1975), 227-259. MR 52:1699
  • 12. Moser, L., Elementary surgery along a torus knot, Pacific J. Math. 38 (1971), 737-745. MR 52:4287
  • 13. Motegi, K., A note on unlinking numbers of Montesinos links, Rev. Mat. Complut. Madrid 9 (1996), 151-164. CMP 97:02
  • 14. Motegi, K., Bridge numbers of twisted Montesinos knots, Proceedings of The Institute of Natural Sciences, Nihon University No. 31 (1996).
  • 15. Murakami, H., Some Metrics on Classical Knots, Math. Ann. 270 (1985), 35-45. MR 86g:57007
  • 16. Rolfsen, D., Knots and links, Mathematics Lecture Series, no.7, Publish or Perish, Berkeley, CA, 1976. MR 58:24236
  • 17. Torisu, I., A note on Montesinos links with unlinking number one (conjectures and partial solutions), Kobe J. of Math. 13 (1996), 167-175.
  • 18. I. Torisu, On nugatory crossings for knots, to appear in Topology and its Appl.

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Additional Information

Ichiro Torisu
Affiliation: Department of Mathematics, Osaka University, Toyonaka, Osaka, 560, Japan
Email: torisu@math.sci.osaka-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-98-04181-1
Received by editor(s): April 8, 1996
Received by editor(s) in revised form: October 22, 1996
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 1998 American Mathematical Society

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