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http://dx.doi.org/10.11568/kjm.2015.23.1.115

THE BASKET NUMBERS OF KNOTS  

Bang, Je-Jun (Gyeongju High School)
Do, Jun-Ho (Gyeongju High School)
Kim, Dongseok (Department of Mathematics Kyonggi University)
Kim, Tae-Hyung (Gyeongju High School)
Park, Se-Han (Gyeongju High School)
Publication Information
Korean Journal of Mathematics / v.23, no.1, 2015 , pp. 115-128 More about this Journal
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 $7_5$.
Keywords
Basket surfaces; Seifert surfaces; Basket numbers;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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