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Knots and complex systems

  • Louis H. Kauffman
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 461-461)

Abstract

This paper is a survey of topics in knot theory from the point of view of complex systems.

Keywords

Braid Group Jones Polynomial Reidemeister Move Lambda Calculus Link Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    P. Aczel, The Theory of Non-Well-Founded Sets, 1988, CLSI Lecture Notes, No. 14.Google Scholar
  2. 2.
    H. P. Barendregt, The Lambda Calculus Its Syntax and Semantics, North Holland, 1981, 1985.Google Scholar
  3. 3.
    “From large cardinals to braids via left distributive algebra”, (to appear in the Journal of Knot Theory and Its Ramifications).Google Scholar
  4. 4.
    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.zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Frederic B. Fitch, Elements of Combinatory Logic, New Haven and London, Yale University Press, 1974.Google Scholar
  6. 6.
    R. H. Fox, Introduction to Knot Theory, Blaisdell Pub. Co., 1963.Google Scholar
  7. 7.
    V. F. R. Jones, “A polynomial invariant of links via von Neumann algebras”, Bull. Amer. Math. Soc., 1985, No. 129, pp. 103–112.CrossRefGoogle Scholar
  8. 8.
    D. Joyce, “A classifying invariant of knots, the knot quandle”, J. Pure and Appl. Algebra, 1983, Vol. 23, pp. 37–65.CrossRefMathSciNetGoogle Scholar
  9. 9.
    L. H. Kauffman, “State models and the Jones polynomial”, Topology, 1987, Vol. 26, pp. 395–407.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    L. H. Kauffman, “Self-Reference and Recursive Forms”, Journal of Social and Biological Structures, 1987, vol. 10, pp. 53–72.CrossRefGoogle Scholar
  11. 11.
    L. H. Kauffman, Knots and Physics, World Scientific Pub., 1991, 1994.Google Scholar
  12. 12.
    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.Google Scholar
  13. 13.
    L. H. Kauffman, “Knot Logic”, To appear in Knots and Applications, edited by L. Kauffman, World Scientific Pub., 1994.Google Scholar
  14. 14.
    L. H. Kauffman and S. W. Winker, Quandles, Crystals and Racks-A New Approach to Knot Theory, (book in preparation), World Scientific Pub.Google Scholar
  15. 15.
    “A calculus for framed links in S3”, Invent. Math. 45 (1978), pp. 35–56.Google Scholar
  16. 16.
    W. B. R. Lickorish, “A representation of orientable, combinatorial three-manifolds”, Ann. of Math. 76 (1962), pp. 531–540.CrossRefMathSciNetGoogle Scholar
  17. 17.
    E. E. Moise, Geometric Topology in Dimensions Two and Three, Springer Verlag, New York, 1977.Google Scholar
  18. 18.
    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.Google Scholar
  19. 19.
    J. H. White, “Self-linking and the Gauss integral in higher dimensions”, Amer. J. Math. 91 (1969), pp. 693–728.zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    S. W. Winker, Quandles, Knot Invariants and the n-fold Branched Cover, (1984), Doctoral Thesis, Univ. of Illinois at Chicago.Google Scholar
  21. 21.
    Edward Witten, “Quantum field theory and the Jones Polynomial”, Commun. Math. Phys., vol. 121, 1989, pp. 351–399.zbMATHCrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Louis H. Kauffman
    • 1
  1. 1.Department of Mathematics, Statistics and Computer ScienceUniversity of Illinois at ChicagoChicago

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