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arxiv: math/0505322 · v1 · pith:4HHVLP6Tnew · submitted 2005-05-16 · 🧮 math.GT

All integral slopes can be Seifert fibered slopes for hyperbolic knots

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keywords hyperbolicseifertslopesfiberfiberedintegerknotknots
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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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