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March 2014 Toroidal Seifert fibered surgeries on alternating knots
Kazuhiro Ichihara, In Dae Jong
Proc. Japan Acad. Ser. A Math. Sci. 90(3): 54-56 (March 2014). DOI: 10.3792/pjaa.90.54

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 $|p|, |q| \ge 3$.

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Kazuhiro Ichihara. In Dae Jong. "Toroidal Seifert fibered surgeries on alternating knots." Proc. Japan Acad. Ser. A Math. Sci. 90 (3) 54 - 56, March 2014. https://doi.org/10.3792/pjaa.90.54

Information

Published: March 2014
First available in Project Euclid: 27 February 2014

zbMATH: 1295.57019
MathSciNet: MR3178485
Digital Object Identifier: 10.3792/pjaa.90.54

Subjects:
Primary: 57M50
Secondary: 57M25

Keywords: Alternating knot , Seifert fibered surgery , toroidal surgery

Rights: Copyright © 2014 The Japan Academy

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Vol.90 • No. 3 • March 2014
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