Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials

Details Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials Alexander Polynomial Invariants of Torus Knots T(n,3) and Chebyshev Polynomials

2011-07-27

arxiv.org/abs/1107.5516v1

Ukr. J. Phys., 2011, Vol. 56, no. 7, pp. 680-687

Physics

Mathematical Physics

8 pages, two-column ujp style; http://www.ujp.bitp.kiev.ua

Scientific paper

The explicit formula, which expresses the Alexander polynomials \Delta_{n,3}(t) of torus knots T(n,3) as a sum of the Alexander polynomials \Delta_{k,2}(t) of torus knots T(k,2), is found. Using this result and those from our previous papers, we express the Alexander polynomials \Delta_{n,3}(t) through Chebyshev polynomials. The latter result is extended to general torus knots T(n,l) with n and l coprime.

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