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Symmetric knots satisfy the cabling conjecture

Published online by Cambridge University Press:  01 May 1998

CHUICHIRO HAYASHI  and
KOYA SHIMOKAWA
CHUICHIRO HAYASHI
Affiliation:
Department of Mathematics Faculty of Science, Gakushuin University, 1-5-1 Mejiro Toshima-ku, Tokyo 171, Japan; e-mail: Chuichiro.Hayashi@gakushuin.ac.jp
KOYA SHIMOKAWA
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan; e-mail: simokawa@poisson.ms.u-tokyo.ac.jp
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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.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 123 , Issue 3 , May 1998 , pp. 501 - 529
Copyright
Cambridge Philosophical Society 1998

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