Delta move and polynomial invariants of links
type: Item
instance of: scholarly article
title: Delta move and polynomial invariants of links
zbMATH Open document ID: 1080.57010
author: Taizo Kanenobu
author: Ryo Nikkuni
published in: Topology and its Applications
publication date: 2005-02-22T00:00:00Z
review text: The delta move is an unknotting operation which substitutes a triangular entanglement by its rotation, introduced in [\textit{S. V. Matveev}, Mat. Zametki 42, 268--278 (1987; Zbl 0634.57006), resp., Math. Notes 42, 651--656 (1987; Zbl 0649.57010)], [\textit{H. Murakami} and \textit{Y. Nakanishi}, Math. Ann. 284, 75--89 (1989; Zbl 0646.57005)]. In this paper the authors give the relationship between the HOMFLY polynomials for the delta skein quadruple: namely the polynomials for the original oriented link \(L\), for the link \(M\) obtained by performing the delta move on \(L\), and smoothings \(L_0\) and \(M_0\), in the case that the arcs involved in the delta move belong to the same component. Using the relation, the authors also give the relationship between other finite type invariants for the quadruple. They further obtain a formula for the zero coefficient polynomials for the twist knots.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 2136457
zbMATH Keywords: Homfly polynomials
zbMATH Keywords: finite type invariants
reviewed by: Johanna Bapt. Marta Asaeda OSB
MaRDI profile type: Publication
full work available at URL: j.topol.2003.02.003
OpenAlex ID: W2018204186
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DOI: 10.1016/J.TOPOL.2003.02.003
description: scientific article; zbMATH DE number 2136457