## Algebraic & Geometric Topology

### All integral slopes can be Seifert fibered slopes for hyperbolic knots

#### 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 $n∈ℤ$, 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

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

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

https://projecteuclid.org/euclid.agt/1513796405

Digital Object Identifier
doi:10.2140/agt.2005.5.369

Mathematical Reviews number (MathSciNet)
MR2135556

Zentralblatt MATH identifier
1083.57012

#### Citation

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. https://projecteuclid.org/euclid.agt/1513796405

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