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Cerf C, Stasiak A. A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links. Proc Natl Acad Sci U S A. 2000;97(8):3795-8doi: 10.1073/pnas.97.8.3795.
Cerf, C., & Stasiak, A. (2000). A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links. Proceedings of the National Academy of Sciences of the United States of America, 97(8), 3795-8. https://doi.org/10.1073/pnas.97.8.3795
Cerf, C, and Stasiak, A. "A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links." Proceedings of the National Academy of Sciences of the United States of America vol. 97,8 (2000): 3795-8. doi: https://doi.org/10.1073/pnas.97.8.3795
Cerf C, Stasiak A. A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links. Proc Natl Acad Sci U S A. 2000 Apr 11;97(8):3795-8. doi: 10.1073/pnas.97.8.3795. PMID: 10760252; PMCID: PMC18095.
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Proc Natl Acad Sci U S A. 2000 Apr 11;97(8):3795-8. doi: 10.1073/pnas.97.8.3795.

A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links.

Proceedings of the National Academy of Sciences of the United States of America

C Cerf, A Stasiak

Affiliations

  1. Departement de Mathematique, Universite Libre de Bruxelles, B-1050 Bruxelles, Belgium.

PMID: 10760252 PMCID: PMC18095 DOI: 10.1073/pnas.97.8.3795

Abstract

We present herein a topological invariant of oriented alternating knots and links that predicts the three-dimensional (3D) writhe of the ideal geometrical configuration of the considered knot/link. The fact that we can correlate a geometrical property of a given configuration with a topological invariant supports the notion that the ideal configuration contains important information about knots and links. The importance of the concept of ideal configuration was already suggested by the good correlation between the 3D writhe of ideal knot configurations and the ensemble average of the 3D writhe of random configurations of the considered knots. The values of the new invariant are quantized: multiples of 4/7 for links with an odd number of components (including knots) and 2/7 plus multiples of 4/7 for links with an even number of components.

References

  1. Biophys J. 1998 Jun;74(6):2815-22 - PubMed
  2. Proc Natl Acad Sci U S A. 1971 Apr;68(4):815-9 - PubMed

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