Constructing a polynomial whose nodal set is the three-twist knot 52

DOI10.1088/1751-8121/aa6cbezbMath1397.57008arXiv1612.06801OpenAlexW3098785788MaRDI QIDQ5348318

Benjamin Bode, Mark Dennis

Publication date: 15 August 2017

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.06801

zbMATH Keywords

phaseknottopologybraidnon-fibered

Mathematics Subject Classification ID

Related Items (7)

Knotted fields and explicit fibrations for lemniscate knots ⋮ On real algebraic links in the 3-sphere associated with mixed polynomials ⋮ Constructing a polynomial whose nodal set is any prescribed knot or link ⋮ Constructing links of isolated singularities of polynomials ℝ4 → ℝ2 ⋮ Aspects of defect topology in smectic liquid crystals ⋮ 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

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• 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
• All knots are algebraic
• Le nœud huit est algébrique réel
• Knot theory realizations in nematic colloids
• Topological events on wave dislocation lines: birth and death of loops, and reconnection
• Cabling in the Skyrme–Faddeev model
• Knotted and linked phase singularities in monochromatic waves
• Knotted fields and explicit fibrations for lemniscate knots
• Knots in the Skyrme–Faddeev model
• Braid Groups
• Singular Points of Complex Hypersurfaces. (AM-61)

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