Proceedings of the Japan Academy, Series A, Mathematical Sciences

Toroidal Seifert fibered surgeries on alternating knots

Kazuhiro Ichihara and In Dae Jong

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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

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

First available in Project Euclid: 27 February 2014

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Zentralblatt MATH identifier

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

Seifert fibered surgery toroidal surgery alternating knot


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.

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