Nullification number and flyping conjecture
type: Item
instance of: scholarly article
title: Nullification number and flyping conjecture
zbMATH Open document ID: 0754.57003
author: Dino Sola
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1992-09-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108235
review text: In analogy to the unknotting number of a knot or link, in the present paper a nullification number is introduced and discussed. For a planar projection of a link, this is the minimal number of ``nullifications'' of crossings which are needed to arrive at a trivial link. For minimal alternating projections this number is easy to compute and depends only on the link. The alternating links with nullification number 1, 2 and \(n- 1\) are classified where \(n\) denotes the number of crossings of the link. It follows that these links have a unique alternating projection, thus confirming the ``Tait flyping conjecture'' for these links. Note that recently a complete solution of this conjecture has been announced by \textit{W. W. Menasco} and \textit{M. B. Thistlethwaite} [Bull. Am. Math. Soc. 25, No. 2, 403-412 (1991; Zbl 0745.57002)] stating that alternating projections of links are basically unique.
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 60475
zbMATH Keywords: minimal projection
zbMATH Keywords: Tait flyping conjecture
zbMATH Keywords: nullification number
zbMATH Keywords: alternating links
reviewed by: Bruno Zimmermann
MaRDI profile type: Publication
cites work: Knots
cites work: State models and the Jones polynomial
cites work: A polynomial invariant of oriented links
cites work: Jones polynomials and classical conjectures in knot theory
cites work: Q4107635
description: scientific article; zbMATH DE number 60475