All integral slopes can be Seifert fibered slopes for hyperbolic knots
Kimihiko Motegi, Hyun-Jong Song
Abstract
Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S3? It is conjectured that if r-surgery on a hyperbolic knot in S3 yields a Seifert fiber space, then r is an integer. We show that for each integer n, there exists a tunnel number one, hyperbolic knot Kn in S3 such that n-surgery on Kn produces a small Seifert fiber space.
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