The Jones polynomial of an unknotting number one knot
type: Item
instance of: scholarly article
title: The Jones polynomial of an unknotting number one knot
zbMATH Open document ID: 0920.57001
DOI: 10.1016/S0166-8641(97)00107-7
author: Yasuyuki Miyazawa
published in: Topology and its Applications
publication date: 1999-09-09T00:00:00Z
review text: The author presents a necessary condition for a knot in \(S^3\) to have unknotting number one, involving the Jones polynomial, the Conway polynomial and the signature. The condition is derived from surgery formulas for the Casson invariant of the 2-fold branched cover of \(S^3\) branched over the knot [cf. \textit{S. Boyer} and \textit{D. Lines}, J. Reine Angew. Math. 405, 181-220 (1990; Zbl 0691.57004); \textit{D. Mullins}, Topology 32, No. 2, 419-438 (1993; Zbl 0784.57003); the author, Osaka J. Math. 32, No. 1, 193-206 (1995; Zbl 0861.57014)].
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 1308036
zbMATH Keywords: Conway polynomial
zbMATH Keywords: signature
zbMATH Keywords: Casson invariant
reviewed by: L. Traldi
MaRDI profile type: Publication
cites work: Q3995494
cites work: Q3033002
cites work: Unknotting Information from 4-Manifolds
cites work: A Family of Links and the Conway Calculus
cites work: Q4775913
cites work: Hecke algebra representations of braid groups and link polynomials
cites work: Two-Bridge Knots with Unknotting Number One
cites work: Q4845496
cites work: Q3746512
cites work: Arf invariants of strongly invertible knots obtained from unknotting number one knots
cites work: Q4089518
cites work: The generalized Casson invariant for 2-fold branched covers of \(S^ 3\) and the Jones polynomial
cites work: On a Certain Numerical Invariant of Link Types
cites work: Q3938886
cites work: Q4107635
cites work: An Extension of Casson's Invariant. (AM-126)
Wikidata QID: Q126556638
description: scientific article; zbMATH DE number 1308036