Korean J. Math. Vol. 23 No. 1 (2015) pp.115-128
DOI: https://doi.org/10.11568/kjm.2015.23.1.115

The basket numbers of knots

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Published: Mar 30, 2015
Keywords:
Basket surfaces, Seifert surfaces, Basket numbers
Mathematics Subject Classification:
57M25, 57M27

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Je-Jun Bang
Gyeongju High School Gyeongju, 780-956, Korea
Jun-Ho Do
Gyeongju High School Gyeongju, 780-956, Korea
Dongseok Kim
Department of Mathematics Kyonggi University Suwon, 443-760 Korea
Tae-Hyung Kim
Gyeongju High School Gyeongju, 780-956, Korea
Se-Han Park
Gyeongju High School Gyeongju, 780-956, Korea

Abstract

Plumbing surfaces of links were introduced to study the geometry of the complement of the links. A basket surface is one of these plumbing surfaces and it can be presented by two sequential presentations, the first sequence is the flat plumbing basket code found by Furihata, Hirasawa and Kobayashi and the second sequence presents the number of the full twists for each of annuli. The minimum number of plumbings to obtain a basket surface of a knot is defined to be the basket number of the given knot. In present article, we first find a classification theorem about the basket number of knots. We use these sequential presentations and the classification theorem to find the basket number of all prime knots whose crossing number is $7$ or less except two knots $7_1$ and $7_5$.


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