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Transactions of the American Mathematical Society

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Composite ribbon number one knots have two-bridge summands


Authors: Steven A. Bleiler and Mario Eudave Muñoz
Journal: Trans. Amer. Math. Soc. 321 (1990), 231-243
MSC: Primary 57M25
DOI: https://doi.org/10.1090/S0002-9947-1990-0968881-9
MathSciNet review: 968881
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Abstract: A composite ribbon knot which can be sliced with a single band move has a two-bridge summand.


References [Enhancements On Off] (What's this?)

  • [BS] S. A. Bleiler and M. G. Scharlemann, A projective plane in $ {R^4}$ with three critical points is standard, MSRI preprint 07112-85; Topology 27 (1988), 519-540. MR 976593 (90e:57006)
  • [CGLS] M. Culler, C. Gordon, J. Luecke, and P. Shalen, Dehn surgery on knots, Ann. of Math. 125 (1987), 237-300. MR 881270 (88a:57026)
  • [Sc$ _{1}$] M. G. Scharlemann, Smooth spheres in $ {R^4}$ with four critical points are standard, Invent. Math. 79 (1985), 125-141. MR 774532 (86e:57010)
  • [Sc$ _{2}$] -, Unknotting number one knots are prime, Invent. Math. 82 (1985), 37-55. MR 808108 (86m:57010)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0968881-9
Keywords: Ribbon knot, ribbon number, Scharlemann cycle, pure level circuit
Article copyright: © Copyright 1990 American Mathematical Society

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