Abstract
This paper is a survey of topics in knot theory from the point of view of complex systems.
Preview
Unable to display preview. Download preview PDF.
References
P. Aczel, The Theory of Non-Well-Founded Sets, 1988, CLSI Lecture Notes, No. 14.
H. P. Barendregt, The Lambda Calculus Its Syntax and Semantics, North Holland, 1981, 1985.
“From large cardinals to braids via left distributive algebra”, (to appear in the Journal of Knot Theory and Its Ramifications).
R. A. Fenn and C. P. Rourke, “Racks and links in codimension two”, J. Knot Theory and its Ramif., 1992, Vol. 1, No. 4, pp. 343–406.
Frederic B. Fitch, Elements of Combinatory Logic, New Haven and London, Yale University Press, 1974.
R. H. Fox, Introduction to Knot Theory, Blaisdell Pub. Co., 1963.
V. F. R. Jones, “A polynomial invariant of links via von Neumann algebras”, Bull. Amer. Math. Soc., 1985, No. 129, pp. 103–112.
D. Joyce, “A classifying invariant of knots, the knot quandle”, J. Pure and Appl. Algebra, 1983, Vol. 23, pp. 37–65.
L. H. Kauffman, “State models and the Jones polynomial”, Topology, 1987, Vol. 26, pp. 395–407.
L. H. Kauffman, “Self-Reference and Recursive Forms”, Journal of Social and Biological Structures, 1987, vol. 10, pp. 53–72.
L. H. Kauffman, Knots and Physics, World Scientific Pub., 1991, 1994.
L. H. Kauffman and S. L. Lins, Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds, Annals of Mathematics Study 114, Princeton Univ. Press, 1994.
L. H. Kauffman, “Knot Logic”, To appear in Knots and Applications, edited by L. Kauffman, World Scientific Pub., 1994.
L. H. Kauffman and S. W. Winker, Quandles, Crystals and Racks-A New Approach to Knot Theory, (book in preparation), World Scientific Pub.
“A calculus for framed links in S3”, Invent. Math. 45 (1978), pp. 35–56.
W. B. R. Lickorish, “A representation of orientable, combinatorial three-manifolds”, Ann. of Math. 76 (1962), pp. 531–540.
E. E. Moise, Geometric Topology in Dimensions Two and Three, Springer Verlag, New York, 1977.
A. Pedretti, Self-Reference on the Isle of Wight—Transcripts of the First International Conference on Self-Reference, (August 24–27, 1979), Princelet Editions London and Zurich.
J. H. White, “Self-linking and the Gauss integral in higher dimensions”, Amer. J. Math. 91 (1969), pp. 693–728.
S. W. Winker, Quandles, Knot Invariants and the n-fold Branched Cover, (1984), Doctoral Thesis, Univ. of Illinois at Chicago.
Edward Witten, “Quantum field theory and the Jones Polynomial”, Commun. Math. Phys., vol. 121, 1989, pp. 351–399.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kauffman, L.H. (1995). Knots and complex systems. In: López-Peña, R., Waelbroeck, H., Capovilla, R., García-Pelayo, R., Zertuche, F. (eds) Complex Systems and Binary Networks. Lecture Notes in Physics, vol 461-461. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103570
Download citation
DOI: https://doi.org/10.1007/BFb0103570
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60339-9
Online ISBN: 978-3-540-44937-9
eBook Packages: Springer Book Archive