Seifert fibered surgery manifolds of composite knots

Abstract

A classification is given for the composite knots and the Dehn surgery on these knots which yield Seifert fibered surgery manifolds. We prove that if a knot K K is the composition of two torus knots, then some (unique) integral surgery on K K yields a Seifert fibered manifold, and conversely if the surgery manifold of a composite knot K K is Seifert fibered, then K K is the composition of two torus knots and the surgery must be integral surgery, which is uniquely determined.