Knotted fields and explicit fibrations for lemniscate knots

DOI10.1098/rspa.2016.0829zbMath1402.57006arXiv1611.02563OpenAlexW2557155427WikidataQ52583115 ScholiaQ52583115MaRDI QIDQ4557912

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Publication date: 27 November 2018

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1611.02563

zbMATH Keywords

knotsingularitybraidapplied topology

Mathematics Subject Classification ID

Related Items (9)

Constructing a polynomial whose nodal set is the three-twist knot 5₂ ⋮ The decay of Hopf solitons in the Skyrme model ⋮ Braided open book decompositions in \(S^{3}\) ⋮ When do knots in light stay knotted? ⋮ Real algebraic links in S3 and braid group actions on the set of n-adic integers ⋮ Constructing a polynomial whose nodal set is any prescribed knot or link ⋮ Constructing links of isolated singularities of polynomials ℝ4 → ℝ2 ⋮ Knotted surfaces as vanishing sets of polynomials ⋮ Maxwell’s theory of solid angle and the construction of knotted fields

Uses Software

• Knot Atlas
• KnotInfo

Cites Work

• Isolated critical points of mappings from \({\mathbb{R}}^ 4\) to \({\mathbb{R}}^ 2\) and a natural splitting of the Milnor number of a classical fibered link. I: Basic theory; examples
• Spiral knots
• A formula for the braid index of links
• A spanning tree expansion of the Jones polynomial
• State models and the Jones polynomial
• Jones polynomials and classical conjectures in knot theory
• Kauffman's polynomial and alternating links
• All knots are algebraic
• Le nœud huit est algébrique réel
• On periodic knots
• Deformations of spaces of imbeddings
• The Jones polynomial for fluid knots from helicity
• Jones polynomials and classical conjectures in knot theory. II
• On the Braid Index of Alternating Links
• Knotted and linked phase singularities in monochromatic waves
• Constructing a polynomial whose nodal set is the three-twist knot 5₂
• Knots in the Skyrme–Faddeev model
• Braid Groups
• The degree of knottedness of tangled vortex lines
• Singular Points of Complex Hypersurfaces. (AM-61)
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