Volume 5, issue 1 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
All integral slopes can be Seifert fibered slopes for hyperbolic knots

Kimihiko Motegi and Hyun-Jong Song

Algebraic & Geometric Topology 5 (2005) 369–378

arXiv: math.GT/0505322

Abstract

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

Keywords
Dehn surgery, hyperbolic knot, Seifert fiber space, surgery slopes
Mathematical Subject Classification 2000
Primary: 57M25, 57M50
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Publication
Received: 10 March 2005
Revised: 25 March 2005
Accepted: 12 April 2005
Published: 30 April 2005
Authors
Kimihiko Motegi
Department of Mathematics
Nihon University
Tokyo 156-8550
Japan
Hyun-Jong Song
Division of Mathematical Sciences
Pukyong National University
599-1 Daeyondong
Namgu
Pusan 608-737
Korea