Seifert fibered surgery manifolds of composite knots

Kalliongis, John; Tsau, Chichen M.

doi:10.1090/S0002-9939-1990-1002161-6

Seifert fibered surgery manifolds of composite knots
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by John Kalliongis and Chichen M. Tsau PDF

Proc. Amer. Math. Soc. 108 (1990), 1047-1053 Request permission

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 $K$ is the composition of two torus knots, then some (unique) integral surgery on $K$ yields a Seifert fibered manifold, and conversely if the surgery manifold of a composite knot $K$ is Seifert fibered, then $K$ is the composition of two torus knots and the surgery must be integral surgery, which is uniquely determined.

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