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The computation of the non-commutative generalization of the A-polynomial for the figure-eight knot

Razvan Gelca·Jeremy Sain
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Abstract

The paper contains the computation of the noncommutative A-ideal of the figure-eight knot, a noncommutative generalization of the A-polynomial. We show that if a knot has the same noncommutative A-ideal as the figure-eight knot, then all colored Kauffman brackets are the same as those of the figure-eight knot.

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Razvan Gelca, Jeremy Sain. 2003-01-24. The computation of the non-commutative generalization of the A-polynomial for the figure-eight knot. https://arxiv.org/abs/math/0301287

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