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THE NONCOMMUTATIVE A-IDEAL OF A (2, 2p + 1)-TORUS KNOT DETERMINES ITS JONES POLYNOMIAL

RĂZVAN GELCA

Department of Mathematics and Statistics, Texas Tech Universitv, Lubbock, TX 79409, USA

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and

JEREMY SAIN

Department of Mathematics and Statistics, Texas Tech Universitv, Lubbock, TX 79409, USA

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https://doi.org/10.1142/S021821650300238XCited by:36 (Source: Crossref)

Abstract

The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same noncommutative A-ideal as the (2,2p + 1)-torus knot has the same colored Jones polynomials. This is a consequence of the orthogonality relation, which yields a recursive relation for computing all colored Jones polynomials of the knot.

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