On T(n, 4) Torus Knots and Chebyshev Polynomials

Authors

  • A.M. Pavlyuk Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine

DOI:

https://doi.org/10.15407/ujpe57.4.439

Keywords:

-

Abstract

The Alexander polynomials ∆n,3(t) and ∆n,4(t) are presented as a sum of the Alexander polynomials ∆k,2(t). These polynomials are also expressed in the form of a sum of Chebyshev polynomials of the second kind. These expansions allow one to introduce the "coordinates" in corresponding bases, which are proposed to be the numerical invariants characterizing links and knots.

References

W.H. Thomson, Proc. of Roy. Soc. Edinburg 6, 94 (1867).

https://doi.org/10.1017/S0370164600045430

L.D. Faddeev, Quantization of Solitons, Preprint IAS-75-QS70 (Inst. for Advanced Study, Princeton, 1975).

E. Witten, Comm. Math. Phys. 121, 351 (1989).

https://doi.org/10.1007/BF01217730

M.F. Atiyah, The Geometry and Physics of Knots (Cambridge Univ. Press, Cambridge, 1990).

https://doi.org/10.1017/CBO9780511623868

L.H. Kauffman, Knots and Physics (World Sci., Singapore, 2001).

https://doi.org/10.1142/4256

E. Radu and M.S. Volkov, Phys. Rep. 468, No. 4, 101 (2008); arXiv:0804.1357v2 [hep-th].

https://doi.org/10.1016/j.physrep.2008.07.002

L. Faddeev and A.J. Niemi, Nature 387, 58 (1997); arXiv:hep-th/9610193.

https://doi.org/10.1038/387058a0

A.M. Gavrilik and A.M. Pavlyuk, Ukr. J. Phys. 55, 129 (2010); arXiv:0912.4674v2 [math-ph].

A.M. Gavrilik, J. Phys. A 27, 91 (1994)

https://doi.org/10.1016/S0022-0736(94)80058-8

Nucl. Phys. B (Proc. Suppl.) 102, 298 (2001), arXiv:hep-th/0103325v4.

D. Rolfsen, Knots and Links (Amer. Math. Soc., Providence, RI, 2003).

https://doi.org/10.1090/chel/346

W.B.R. Lickorish, An Introduction to Knot Theory (Springer, New York, 1997).

https://doi.org/10.1007/978-1-4612-0691-0

A.M. Gavrilik and A.M. Pavlyuk, Ukr. J. Phys. 56, 680 (2011); arXiv:1107.5516v1 [math-ph].

Downloads

Published

2012-04-30

How to Cite

Pavlyuk, A. (2012). On T(n, 4) Torus Knots and Chebyshev Polynomials. Ukrainian Journal of Physics, 57(4), 439. https://doi.org/10.15407/ujpe57.4.439

Issue

Section

General problems of theoretical physics