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.

Notes on file formats

Kimihiko Motegi, Hyun-Jong Song
Department of Mathematics, Nihon University
Tokyo 156-8550, Japan
and
Division of Mathematical Sciences, Pukyong National University
599-1 Daeyondong, Namgu, Pusan 608-737, Korea
Email: motegi@math.chs.nihon-u.ac.jp, hjsong@pknu.ac.kr

AGT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to http://msp.warwick.ac.uk/.