Algebraic & Geometric Topology

All integral slopes can be Seifert fibered slopes for hyperbolic knots

Kimihiko Motegi and Hyun-Jong Song

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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.

Article information

Algebr. Geom. Topol., Volume 5, Number 1 (2005), 369-378.

Received: 10 March 2005
Revised: 25 March 2005
Accepted: 12 April 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M50: Geometric structures on low-dimensional manifolds

Dehn surgery hyperbolic knot Seifert fiber space surgery slopes


Motegi, Kimihiko; Song, Hyun-Jong. All integral slopes can be Seifert fibered slopes for hyperbolic knots. Algebr. Geom. Topol. 5 (2005), no. 1, 369--378. doi:10.2140/agt.2005.5.369.

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