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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 7, p.673-676


Pavlyuk A.M.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: pavlyuk@bitp.kiev.ua)

Generalization of Polynomial Invariants and Holographic Principle for Knots and Links

Section: General problems of theoretical physics
Original Author's Text: English

Abstract: We formulate the holographic principle for knots and links. For the “space” of all knots and links, torus knots T(2m + 1, 2 ) and torus links L(2m, 2 ) play the role of the “boundary” of this space. Using the holographic principle, we find the skein relation of knots and links with the help of the recurrence relation for polynomial invariants of torus knots T(2m + 1, 2 ) and torus links L(2m, 2 ). As an example of the application of this principle, we derive the Jones skein relation and its generalization with the help of some variants of (q, p)-numbers, related with (q, p)-deformed bosonic oscillators.

Key words: holographic principle, knots, links, Jones skein relation.