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

Je-Jun Bang, Jun-Ho Do, Dongseok Kim, Tae-Hyung Kim, Se-Han Park

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

Subject classification

57M25, 57M27

Sponsor(s)



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References


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