All integral slopes can be Seifert fibered slopes for hyperbolic knots

Motegi, Kimihiko¹ ; Song, Hyun-Jong²

¹Department of Mathematics, Nihon University, Tokyo 156-8550, Japan
²Division of Mathematical Sciences, Pukyong National University, 599-1 Daeyondong, Namgu, Pusan 608-737, Korea

Algebraic and Geometric Topology, Tome 5 (2005) no. 1, pp. 369-378

Résumé

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 ∈ ℤ, there exists a tunnel number one, hyperbolic knot Kn in S3 such that n–surgery on Kn produces a small Seifert fiber space.

Détail

DOI : 10.2140/agt.2005.5.369

Keywords: Dehn surgery, hyperbolic knot, Seifert fiber space, surgery slopes

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