Natural classification of knots

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 463, Issue 2078, 2007, Pages 569-582

  Flammini, Alessandro ^a   Stasiak, Andrzej ^b  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITY OF LAUSANNE   (Switzerland)

Author keywords

Knot invariants; Knots; Topology

Indexed keywords

EID: 36348967241     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2006.1782     Document Type: Article

References (23)

1. Adams, C. C. 1994 The knot book. New York, NY: W.H. Freeman and Company.
2. Buniy, R. & Kephart, T. 2003 A model of glueballs. Phys. Lett. B 576, 127-134. (doi:10.1016/j.physletb.2003.09.081)
3. Buniy, R. & Kephart, T. 2005 Glueballs and the universal energy spectrum of tight knots and links. Int. J. Mod. Phys. A 20, 1252-1259. (doi:10.1142/S0217751X05024146)
4. Cerf, C. & Stasiak, A. 2000 A topological invariant to predict the three-dimensional writhe of ideal configurations of knots and links. Proc. Natl Acad. Sci. USA 97, 3795-3798. (doi:10.1073/pnas.97.8.3795)
5. Cerf, C. & Stasiak, A. 2003 Linear relations between writhe and minimal crossing number in Conway families of ideal knots and links. New J. Phys. 5, 87.1-87.15. (doi:10.1088/1367-2630/5/1/387)
6. Darcy, I. K.&Sumners, D. W. 1997Astrand passsage metrics for topoisomerase action. In Knots '96: Proc. Fifth Int. Research Institute of Mathematical Society of Japan (ed. S. Suzuki), pp. 267-278. Singapore: World Scientific.
7. Darcy, I. K. & Sumners, D. W. 2000 Rational tangle distance on knots and links. Math. Proc. Camb. Phil. Soc. 128, 497-510. (doi:10.1017/S0305004199004375)
8. Devlin, K. 2001 Round the twist. New Sci. 172, 40-42.
9. Dobay, A., Dubochet, J., Millett, K., Sottas, P. E. & Stasiak, A. 2003 Scaling behavior of random knots. Proc. Natl Acad. Sci. USA 100, 5611-5615. (doi:10.1073/pnas.0330884100)
10. Ewing, B. & Millett, K. C. 1996 Computational algorithms and the complexity of link polynomials. In Progress in Knot Theory and Related Topics, pp. 51-68. Paris, France: Hermann.
11. Faddeev, L. D. & Niemi, A. J. 1997 Stable knot-like structures in classical field theory. Nature 387, 58-61. (doi:10.1038/387058a0)
12. Flammini, A., Maritan, A. & Stasiak, A. 2004 Simulations of action of DNA topoisomerases to investigate boundaries and shapes of spaces of knots. Biophys. J 87, 2968-2975. (doi:10.1529/biophysj.104.045864)
13. Freyd, P., Yetter, D., Hoste, J., Lickorish, W., Millett, K. & Ocneau, A. 1985 A new polynomial invariant of knots and links. Bull. Am. Math. Soc. 12, 239-246.
14. Katritch, V., Bednar, J., Michoud, D., Scharein, R. G., Dubochet, J. & Stasiak, A. 1996 Geometry and physics of knots. Nature 384, 142-145. (doi:10.1038/384142a0)
15. Katritch, V., Olson, W. K., Pieranski, P., Dubochet, J. & Stasiak, A. 1997 Properties of ideal composite knots. Nature 388, 148-151. (doi:10.1038/40582)
16. Moffatt, H. K. 1990 The energy spectrum of knots and links. Nature 347, 367-369. (doi:10.1038/347367a0)
17. Pieranski, P. 1998 In search of ideal knots. In Ideal knots, vol. 19 (ed. A. Stasiak, V. Katritch & L. H. Kauffman), pp. 20-41. Singapore: World Scientific.
18. Pieranski, P. & Przybyl, S. 2001 Quasi-quantization of writhe in ideal knots. Eur. Phys. J. E - Soft Matter 6, 117-121. (doi:10.1007/s101890170011)
19. Ralston, J. P. 2003 The Bohr atom of glueballs. arxiv.org/abs/hep-ph/ 0301089.
20. Rolfsen, D. 1976 Knots and links. Berkeley, CA: Publish or Perish Press.
21. Stasiak, A. 2000 Quantum-like properties of knots and links. In Knots in Hellas '98 (ed. C. M. Gordon, V. F. R. Jones, L. H. Kauffman, S. Lambropolu & J. H. Przytycki), pp. 477-500. Singapore: World Scientific.
22. Thomson, W. H. 1869 On vortex motion. Trans. R. Soc. Edin. 25, 217-260.
23. Vologodskii, A. V., Levene, S. D., Klenin, K. V., Frank-Kamenetskii, M. & Cozzarelli, N. R. 1992 Conformational and thermodynamic properties of supercoiled DNA. J. Mol. Biol. 227, 1224-1243. (doi:10.1016/0022-2836(92)90533-P)