## Proceedings of the Japan Academy, Series A, Mathematical Sciences

### Toroidal Seifert fibered surgeries on alternating knots

#### Abstract

We give a complete classification of toroidal Seifert fibered surgeries on alternating knots. Precisely, we show that if an alternating knot $K$ admits a toroidal Seifert fibered surgery, then $K$ is either the trefoil knot and the surgery slope is zero, or the connected sum of a $(2,p)$-torus knot and a $(2,q)$-torus knot and the surgery slope is $2(p+q)$ with $|p|, |q| \ge 3$.

#### Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 90, Number 3 (2014), 54-56.

Dates
First available in Project Euclid: 27 February 2014

Permanent link to this document
http://projecteuclid.org/euclid.pja/1393510215

Digital Object Identifier
doi:10.3792/pjaa.90.54

Mathematical Reviews number (MathSciNet)
MR3178485

Zentralblatt MATH identifier
1295.57019

#### Citation

Ichihara, Kazuhiro; Jong, In Dae. Toroidal Seifert fibered surgeries on alternating knots. Proc. Japan Acad. Ser. A Math. Sci. 90 (2014), no. 3, 54--56. doi:10.3792/pjaa.90.54. http://projecteuclid.org/euclid.pja/1393510215.

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