Symmetric knots satisfy the cabling conjecture
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)
1 This research was partially supported by Fellowships of the Japan Society for the Promotion of Science for Japanese Junior Scientists.