Fetching the paper…
Reading the bibliography…
We give an explicit construction of complex maps whose nodal line have the form of lemniscate knots.
Brauner K. 1928. Zur Geometrie der Funktionen zweier komplexen Veränderlichen II, III, IV. Abh Math Sem Hamburg
1928
Earlier work this paper cites.
Kähler E. 1929. Über die Verzweigung einer algebraischen Funktion zweier Veränderlichen in der Umgebung einer singulären Stelle. Math Zeit
1929
Earlier work this paper cites.
Zariski O. 1932. On the topology of algebroid singularities. Am J of Math
1932
Earlier work this paper cites.
Burau K. 1933. Kennzeichnung von Schlauchknoten. Abh Math Sem Hamburg
1933
Earlier work this paper cites.
Burau K. 1934. Kennzeichnung von Schlauchverkettungen. Abh Math Sem Hamburg
1934
Earlier work this paper cites.
Ehresmann C. 1950. Les connexions infinitésimales dans un espace fibré différentiable. Colloque de Topologie
1950
Earlier work this paper cites.
Milnor JW. 1968. Singular points of complex hypersurfaces
1968
Earlier work this paper cites.
Moffatt HK. 1969. The degree of knottedness of tangled vortex lines. J Fluid Mech
1969
Earlier work this paper cites.
Murasugi K. 1971. On periodic knots. Commentarii Mathematici Helvetici
1971
Earlier work this paper cites.
Edwards RD, Kirby RC. 1971. Deformations of spaces of imbeddings. Ann Math (2ns Series)
1971
Earlier work this paper cites.
Looijenga E. 1971. A note on polynomial isolated singularities. Ind Math (Proc)
1971
Earlier work this paper cites.
Lê, DT. 1972. Sur les noeuds algébriques. Comp Math
1972
Earlier work this paper cites.
Faddeev LD. 1975. Quantization of solitons. Princeton Preprint IAS-75-QS70
1975
Earlier work this paper cites.
Stallings JR. 1978. Constructions of fibred knots and links. Proceedings of Symposia in Pure Mathematics
1978
Earlier work this paper cites.
Akbulut S, King HC. 1981. All knots are algebraic. Commentarii Mathematici Helvetici
1981
Earlier work this paper cites.
Perron B. 1982. Le nœud “huit” est algébrique réel. Inv Math
1982
Earlier work this paper cites.
Bott R, Tu LW. 1982. Differential forms in algebraic topology
1982
Earlier work this paper cites.
Rudolph L. 1984. Review of “Le nœud “huit” est algébrique réel” by Perron, B
1984
Earlier work this paper cites.
Eisenbud D, Neumann W. 1985. Three-dimensional link theory and invariants of plane curve singularities
1985
Cited alongside, same era.
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
Cited alongside, same era.
Kauffman LH. 1987. State models and the Jones polynomial. Topology
1987
Cited alongside, same era.
Thistlewaite MB. 1987. A spanning tree expansion of the Jones polynomial. Topology
1987
Cited alongside, same era.
Murasugi K. 1987. The Jones polynomial and classical conjectures in knot theory. Topology
1987
Cited alongside, same era.
Rudolph L. 2005. Knot theory of complex plane curves, in Handbook of Knot Theory
2005
Later among the works it cites.
Sutcliffe P. 2007. Knots in the Skyrme-Faddeev model. Proc R Soc A
2007
Later among the works it cites.
Irvine WTM, Bouwmeester D. 2008. Linked and knotted beams of light. Nature Physics
2008
Later among the works it cites.
Kassel C, Turaev V. 2008. Braid groups
2008
Later among the works it cites.
Dennis MR, King RP, Jack B, O’Holleran K, Padgett MJ. 2010. Isolated opitcal vortex knots. Nature Physics
2010
Later among the works it cites.
Brothers N, Evans S, Tallman L, Van Wyk L, Witzcak D, Yarnall C. 2010. Spiral knots. Missouri J Math Sci
2010
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
1987
Cited alongside, same era.
Thistlewaite MB. 1988. Kauffman’s polynomial and alternating links. Topology
1988
Cited alongside, same era.
Murasugi K. 1991. On the braid index of alternating links. Trans Am Math Soc
1991
Cited alongside, same era.
Livingston C. 1993. Knot theory
1993
Cited alongside, same era.
Winfree AT. 1994. Persistent tangled vortex rings in generic excitable media. Nature
1994
Cited alongside, same era.
Kawauchi A. 1996. Survey of knot theory
1996
Cited alongside, same era.
Bochnak J, Coste M, Roy M-F. 1998. Real algebraic geometry
1998
Cited alongside, same era.
King RP. 2010. Knotting of optical vortices
2010
Later among the works it cites.
Lee SY, Seo M. 2010. A formula for the braid index of links. Topology and its Applications
2010
Later among the works it cites.
Dennis MR, Goette J, King RP, Morgan MA, Alonso MA. 2011. Paraxial and nonparaxial polynomial beams and the analytic approach to propagation. Optics Letters
2011
Later among the works it cites.
Liu X, Ricca RL. 2012. The Jones polynomial for fluid knots from helicity. J Phys A: Math Theor
2012
Later among the works it cites.
Machon T, Alexander GP. 2014. Knotted defects in nematic liquid crystals. Phys Rev Lett
2014
Later among the works it cites.
2016
Closest in time.
Kim SJ, Stees R, Taalman L. 2016. Sequences of spiral knot determinants. Journal of Integer Sequences
2016
Closest in time.
Bar-Natan, D. The Knot Atlas. http://katlas.org/
2016
Closest in time.
Cha JC, Livingston C. KnotInfo: Table of knot invariants. http://www.indiana.edu/ knotinfo
2016
Closest in time.
Taylor AJ, Dennis MR. 2016. Vortex knots in tangled quantum eigenfunctions. Nature Comm
2016
Closest in time.
Soret M, Ville M. 2016. Lissajous-toric knots. arXiv:1610.04418
2016
Closest in time.