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Twisting operations and composite knots

Author: Masakazu Teragaito
Journal: Proc. Amer. Math. Soc. 123 (1995), 1623-1629
MSC: Primary 57M25
MathSciNet review: 1254855
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Abstract: Suppose that a composite knot K in $ {S^3}$ can be changed to a trivial knot by 1/n-surgery along a trivial loop C. We show that $ \vert n\vert \leq 2$. Moreover, if there is a decomposing sphere of K which meets C in two points, then $ \vert n\vert \leq 1$.

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  • [1] M. Culler, C. McA. Gordon, J. Luecke, and P. B. Shalen, Dehn surgery on knots, Ann. of Math. (2) 125 (1987), 237-300. MR 881270 (88a:57026)
  • [2] C. McA. Gordon, When are tori created by Dehn surgery?, Conference Report for the International Conference on Knot Theory and Related Topics, 1990, pp. 18-19.
  • [3] -, Combinatorial methods in knot theory, Algebra and Topology (S. H. Bae and G. T. Jin, eds.), Proc. KAIST Math. Workshop, vol. 5, 1990, pp. 1-23. MR 1098718 (92e:57007)
  • [4] Y. Mathieu, Unknotting, knotting by twists on disks and property (P) for knots in $ {S^3}$, Knots 90 (A. Kawauchi, ed.), Proc. 1990 Osaka Conference on Knot Theory and Related Topics, de Gruyter, Berlin, 1992, pp. 93-102. MR 1177414 (93i:57008)
  • [5] K. Miyazaki and A. Yasuhara, Knots that cannot be obtained from a trivial knot by twisting, preprint, 1993. MR 1282760 (96c:57019)
  • [6] K. Motegi, Primeness of twisted knots, Proc. Amer. Math. Soc. 119 (1993), 979-983. MR 1181171 (94c:57014)
  • [7] K. Motegi and T. Shibuya, Are knots obtained from a plain pattern prime?, Kobe J. Math. 9 (1992), 39-42. MR 1189955 (93i:57009)
  • [8] D. Rolfsen, Knots and links, Math. Lecture Ser., vol. 7, Publish or Perish, Berkeley, CA, 1976. MR 0515288 (58:24236)
  • [9] M. Scharlemann, Unknotting number one knots are prime, Invent. Math. 82 (1985), 37-55. MR 808108 (86m:57010)
  • [10] M. Scharlemann and A. Thompson, Unknotting number, genus, and companion tori, Math. Ann. 280 (1988), 191-205. MR 929535 (89d:57008)
  • [11] M. Teragaito, Composite knots trivialized by twisting, J. Knot Theory Ramifications 1 (1992), 467-470. MR 1194998 (93k:57023)

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Keywords: Knot, twisting
Article copyright: © Copyright 1995 American Mathematical Society

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