Mathematical Proceedings of the Cambridge Philosophical Society



Symmetric knots satisfy the cabling conjecture


CHUICHIRO HAYASHI a1 1 and KOYA SHIMOKAWA a2 1
a1 Department of Mathematics Faculty of Science, Gakushuin University, 1-5-1 Mejiro Toshima-ku, Tokyo 171, Japan; e-mail: Chuichiro.Hayashi@gakushuin.ac.jp
a2 Graduate School of Mathematical Sciences, University of Tokyo, Komaba, Tokyo 153, Japan; e-mail: simokawa@poisson.ms.u-tokyo.ac.jp

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.)

(Received August 7 1995)
(Revised January 7 1997)



Footnotes

1 This research was partially supported by Fellowships of the Japan Society for the Promotion of Science for Japanese Junior Scientists.