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We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot $5_2$.
Brauner K 1928 Zur Geometrie der Funktionen zweier komplexen Veränderlichen II, III, IV. Abh Math Sem Hamburg
1928
Earlier work this paper cites.
Milnor J W 1968 Singular points of complex hypersurfaces
1968
Earlier work this paper cites.
Stallings J R 1978 Constructions of fibred knots and links Proc Symp Pure Math
1978
Earlier work this paper cites.
Akbulut S and King H C 1981 All knots are algebraic Comm Math Helv
1981
Earlier work this paper cites.
Perron B 1982 Le nœud “huit” est algébrique réel Inv Math
1982
Earlier work this paper cites.
Winfree AT and Strogatz SH 1984 Organizing centres for three-dimensional chemical waves Nature
1984
Earlier work this paper cites.
Rudolph L 1987 Isolated critical points of mappings from ℝ 4 \mathbb{R}^{4} to ℝ 2 \mathbb{R}^{2} and a natural splitting of the Milnor number of a classical fibred link : 1. Basic theory and examples Comm Math Helv
1987
Earlier work this paper cites.
Berry M V 2001 Knotted zeros in the quantum states of hydrogen Found Phys
2001
Earlier work this paper cites.
Pajitnov A, Rudolph L and Weber L K 2001 The Morse-Novikov number for knots and links Algebra i Analiz
2002
Earlier work this paper cites.
Rolfsen D 2003 Knots and Links
2003
Earlier work this paper cites.
Sutcliffe PM and Winfree AT 2003 Stability of knots in excitable media Phys. Rev
2003
Earlier work this paper cites.
Gittings T A 2004 Minimum braids: A complete invariant of knots and links arXiv:math.GT/0401051
2004
Cited alongside, same era.
Goda H, 2007 Some estimates of the Morse-Novikov numbers for knots and links, in Intelligence of Low Dimensional Topology 2006
2006
Cited alongside, same era.
Sutcliffe P 2007 Knots in the Skyrme-Faddeev model Proc R Soc A
2007
Cited alongside, same era.
Berry M V and Dennis M R 2007 Topological events on wave dislocation lines: birth and death of loops, and reconnection J. Phys. A: Math. Gen
2007
Cited alongside, same era.
Kassel C and Turaev V 2008 Braid groups
2008
Cited alongside, same era.
Dennis M R, King R P, Jack B, O’Holleran K and Padgett M J 2010 Isolated optical vortex knots Nature Physics
Čopar S, Tkalec U, Muševič I and Žumer S 2015 Knot theory realizations in nematic colloids PNAS
2015
Later among the works it cites.
Bar-Natan, D The Knot Atlas. http://katlas.org/
2016
Closest in time.
Cha J C and Livingston C KnotInfo: Table of knot invariants. http://www.indiana.edu/ knotinfo
2016
Closest in time.
Hall D S, Ray M W, Tiurev K, Ruokekoski E, Gheorghe A H and Möttönen M 2016 Tying quantum knots Nature Physics
2016
Closest in time.
2016
Closest in time.
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2010
Cited alongside, same era.
Dennis M R, Götte J B, King R P, Morgan M A and Alonso M A 2011 Paraxial and nonparaxial polynomial beams and the analytic approach to propagation Opt Lett
2011
Cited alongside, same era.
Kleckner D and Irvine W T M 2013 Creation and dynamics of knotted vortices Nature Physics
2013
Cited alongside, same era.
Kedia H, Bialynicki-Birula I, Peralta-Salas D and Irvine W T M 2013 Tying knots in light fields Phys. Rev. Lett
2013
Cited alongside, same era.
2015
Cited alongside, same era.
Jennings P 2015 Cabling in the Skyrme-Faddeev model J Phys A
2015
Cited alongside, same era.
Cited in the paper.
2016
Closest in time.
Taylor A J and Dennis M R 2016 Vortex knots in tangled quantum eigenfunctions Nature Comm
2016
Closest in time.
Maucher F and Sutcliffe PM 2016 Untangling knots via reaction-diffusion dynamics of vortex strings Phys. Rev. Lett
2016
Closest in time.
Machon T and Alexander G P 2016 Global defect topology in nematic liquid crystals Proc R Soc A
2016
Closest in time.
Kamien R D and Mosna R A 2016 The topology of dislocations in smectic liquid crystals New J Phys
2016
Closest in time.