A relation between the LG polynomial and the Kauffman polynomial
type: Item
instance of: scholarly article
title: A relation between the LG polynomial and the Kauffman polynomial
zbMATH Open document ID: 1126.57003
author: Atsushi Ishii
author: Taizo Kanenobu
published in: Topology and its Applications
publication date: 2007-04-18T00:00:00Z
review text: The authors consider the 2-variable link polynomials of Links and Gould, \(LG_L(t_0,t_1)\), of Kauffman, \(F_L(a,z)\), and the so-called Dubrovnik polynomial, \(Y_L(a,z)\) of an oriented link \(L\) in \(S^3\). The reduced polynomial \(LG_L(t,t)(= KLG_L(t))\) is proved to be equal to suitable reductions of \(F_L\) and \(Y_L\). Using a result of Thistlethwaite on \(F_L (a,z)\) this shows that the crossing number of an adequate link diagram is obtained by \(LG_L\). (A reduced alternating diagram is adequate.) Also the determinant of \(L\) is determined by \(KLG\).
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 5144528
zbMATH Keywords: knots
zbMATH Keywords: links
zbMATH Keywords: the LG polynomial
zbMATH Keywords: the Kauffman polynomial
reviewed by: Gerhard Burde
MaRDI profile type: Publication
full work available at URL: j.topol.2006.04.023
OpenAlex ID: W2033493318
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DOI: 10.1016/J.TOPOL.2006.04.023
description: scientific article; zbMATH DE number 5144528