Communications in Mathematical Physics

, Volume 80, Issue 4, pp 543–553 | Cite as

Rigid curves at random positions and linking numbers

  • J. des Cloizeaux
  • R. Ball


A property of the square of the linking number of two closed rigid curves randomly displaced in a three dimensional space, has been recently found by W. Pohl. Here, this result is reproduced and generalized. This new approach is quite different and uses a simple Fourier transformation.


Neural Network Fourier Fourier Transformation Statistical Physic Complex System 


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    Rolfsen, D.: Knots and Links. Mathematics Lecture Series, Vol. 7, p. 132. Berkeley, CA: Publish or Perish, Inc. 1976Google Scholar
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    Alexandroff, P. and Hopf, H.: Topologie I. Berlin: Springer 1935Google Scholar
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    Pohl, W.: International Symposium in honour of N.H. Kuiper, Utrecht 1980. In: Lecture Notes in Mathematics. Berlin, Heidelberg, New York: Springer (to be published)Google Scholar
  4. 4.
    Duplantier, B.: Linking umbers, contracts, and mutal inductances of a Random set of closed curves. Commun. Math. Phys. (to appear)Google Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • J. des Cloizeaux
    • 1
  • R. Ball
    • 1
  1. 1.Service de Physique ThéoriqueCEN-SaclayGif-sur-YvetteFrance

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