TOROIDAL SURGERY ON PERIODIC KNOTS

We show that r-Dehn surgery on a hyperbolic, periodic knot K with period p> 2 yields a hyperbolic manifold unless p = 3, r = 0 and the genus of K is one. Regarding hyperbolic, periodic knots with period 2, we show that only integral Dehn surgeries can yield toroidal manifolds. 1. Introduction. A 3-manifold is toroidal if it contains an essential torus, i.e., an incompress-ible torus not parallel to a boundary component. A knot K in S3 is called a periodic knot with period p if there is a homeomorphism f: S3 → S3 such that f(K) = K, Fix(f)∩K = ∅, and Fix(f) is a circle. We call f a periodi