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Symmetric knots satisfy the cabling conjecture

  • CHUICHIRO HAYASHI (a1) and KOYA SHIMOKAWA (a2)
    • Published online: 01 May 1998
Abstract

The cabling conjecture states that a non-trivial knot K in the 3-sphere is a cable knot or a torus knot if some Dehn surgery on K yields a reducible 3-manifold. We prove that symmetric knots satisfy this conjecture. (Gordon and Luecke also prove this independently ([GLu3]), by a method different from ours.)

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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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