Algebraic and Geometric Topology 5 (2005), paper no. 16, pages 369-378.

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 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.

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

AMS subject classification. Primary: 57M25, 57M50.

DOI: 10.2140/agt.2005.5.369

E-print: arXiv:math.GT/0505322

Submitted: 10 March 2005. (Revised: 25 March 2005.) Accepted: 12 April 2005. Published: 30 April 2005.

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

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