All integral slopes can be Seifert fibered slopes for hyperbolic knots

Kimihiko Motegi; Hyun-Jong Song

doi:10.2140/agt.2005.5.369

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All integral slopes can be Seifert fibered slopes for hyperbolic knots

Kimihiko Motegi·Hyun-Jong Song

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Abstract

Which slopes can or cannot appear as Seifert fibered slopes for hyperbolic knots in the 3-sphere S^3? It is conjectured that if r-surgery on a hyperbolic knot in S^3 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 K_n in S^3 such that n-surgery on K_n produces a small Seifert fiber space.

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BibTeX RIS

Kimihiko Motegi, Hyun-Jong Song. 2005-05-16. All integral slopes can be Seifert fibered slopes for hyperbolic knots. https://doi.org/10.2140/agt.2005.5.369

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