Links which are related by a band surgery or crossing change
type: Item
instance of: scholarly article
title: Links which are related by a band surgery or crossing change
zbMATH Open document ID: 1310.57014
author: Taizo Kanenobu
author: Hiromasa Moriuchi
published in: Boletín de la Sociedad Matemática Mexicana. Third Series
publication date: 2015-01-09T00:00:00Z
review text: In this paper, the authors develop some criteria for links to be related by a single crossing change or a single band surgery. One is described by using the determinant of a link. More precisely conditions are obtained on the determinant of a link so that the link is related to a 2-bridge knot by a single crossing change (Proposition 4.1) and a single band surgery (Theorem 4.2). Also the authors give such conditions using some special values of the polynomial invariants.
reviewed by: Kazuhiro Ichihara
Mathematics Subject Classification ID: 57M25
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 6384874
zbMATH Keywords: band surgery
zbMATH Keywords: \(H(2)\)-move
MaRDI profile type: Publication
full work available at URL: s40590-014-0032-8
OpenAlex ID: W2152572488
cites work: Unoriented band surgery on knots and links
cites work: Jones' Braid-Plat Formula and a New Surgery Triple
cites work: A polynomial invariant for unoriented knots and links
cites work: Q4829661
cites work: A strand passage metric for topoisomerase action
cites work: BIOLOGICAL DISTANCES ON DNA KNOTS AND LINKS: Applications to XER recombination
cites work: Rational tangle surgery and Xer recombination on catenanes
cites work: Rational tangle distances on knots and links
cites work: NULLIFICATION OF KNOTS AND LINKS
cites work: A new polynomial invariant of knots and links
cites work: Q3290349
cites work: Q3289540
cites work: Unknotting operations involving trivial tangles
cites work: Hecke algebra representations of braid groups and link polynomials
cites work: On a certain value of the Kauffman polynomial
cites work: BAND SURGERY ON KNOTS AND LINKS
cites work: H(2)-GORDIAN DISTANCE OF KNOTS
cites work: Band surgery on knots and links, II
cites work: Q3052515
cites work: \(SH(3)\)-Gordian distances between knots with up to seven crossings
cites work: Q3746512
cites work: A relationship between link polynomials
cites work: Unknotting by adding a Twisted Band
cites work: Q4367595
cites work: Some evaluations of link polynomials
cites work: The Jones polynomial of an unknotting number one knot
cites work: GORDIAN DISTANCE AND POLYNOMIAL INVARIANTS
cites work: Some metrics on classical knots
cites work: On a Certain Numerical Invariant of Link Types
cites work: Q3938886
cites work: Invariants of links of Conway type
cites work: An invariant of knot cobordism
cites work: Q4107635
cites work: Q5749983
cites work: Polynomial values, the linking form and unknotting numbers
cites work: The determination of the pairs of two-bridge knots or links with Gordian distance one
cites work: Q4263296
DOI: 10.1007/S40590-014-0032-8
description: scientific article; zbMATH DE number 6384874