JP Journal of Geometry and Topology
Volume 18, Issue 1, Pages 65 - 84
(August 2015) http://dx.doi.org/10.17654/JPGTAug2015_065_084 |
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ON AN ESTIMATION OF FLAT PLUMBING BASKET NUMBER OF KNOTS
Nao Imoto
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Abstract: For a knot K, Hirose and Nakashima introduced a numerical invariant called flat plumbing basket number, denoted which is the minimal number of annuli to obtain a flat plumbing basket of K. They gave two estimations of using the degree of the Alexander polynomial of K. In this paper, we introduce a basket diagram to represent a basket, which is an extension of a flat plumbing basket diagram, and introduce some operations on basket diagrams. Then we show that one of the estimations given by Hirose and Nakashima is exact by using these operations. |
Keywords and phrases: knots and links, Seifert surface, flat plumbing basket. |
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