#### 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

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