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
Article

Abstract

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.

Keywords

Neural Network Fourier Fourier Transformation Statistical Physic Complex System 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Rolfsen, D.: Knots and Links. Mathematics Lecture Series, Vol. 7, p. 132. Berkeley, CA: Publish or Perish, Inc. 1976Google Scholar
  2. 2.
    Alexandroff, P. and Hopf, H.: Topologie I. Berlin: Springer 1935Google Scholar
  3. 3.
    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

Personalised recommendations