Some relations on Miyazawa's virtual knot invariant
type: Item
instance of: scholarly article
title: Some relations on Miyazawa's virtual knot invariant
zbMATH Open document ID: 1131.57006
author: Naoko Kamada
published in: Topology and its Applications
publication date: 2007-04-18T00:00:00Z
review text: Kauffman defined a polynomial invariant \(f_{L}(A)\in{\mathbb Z}[A^2,A^{-2}]\) for a virtual link \(L\) [\textit{L. H. Kauffman}, Eur. J. Comb. 20, No.~7, 663--690 (1999; Zbl 0938.57006)]. The Miyazawa polynomial \(R_{L}(A,h)\in{\mathbb Z}[A,A^{-1},h]\) is a 2-variable polynomial invariant for virtual links [\textit{N. Kamada} and \textit{Y. Miyazawa}, Hiroshima Math. J. 35, No.~2, 309--326 (2005; Zbl 1093.57007)]. It is equal to \(f_{L}(A)\) after substituting \(1\) for \(h\). In the paper under discussion the author introduces a relation between the Miyazawa polynomials of links in a virtual skein triple. This generalizes results from [\textit{N. Kamada}, Osaka J. Math. 39, No.~2, 325--333 (2002; Zbl 1007.57005)] and [\textit{N. Kamada, S. Nakabo} and \textit{S. Satoh}, Ill. J. Math. 46, No.~2, 467--475 (2002; Zbl 1008.57007)].
reviewed by: Michael Heusener
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 5144529
zbMATH Keywords: Virtual knot theory
MaRDI profile type: Publication
full work available at URL: j.topol.2006.04.025
OpenAlex ID: W1978372075
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cites work: Q3989600
cites work: Virtual knot theory
DOI: 10.1016/J.TOPOL.2006.04.025
description: scientific article; zbMATH DE number 5144529