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The A-polynomial from the noncommutative viewpoint

Charles Frohman·Razvan Gelca·Walter Lofaro
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Abstract

We develop an invariant of knots that depends on a complex parameter t, describing a left ideal in the noncommutative torus. When the parameter is set equal to -1 we recover the A-polynomial of the knot. We relate the invariant to the colored Jones polynomials of the knot.

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Charles Frohman, Razvan Gelca, Walter Lofaro. 1998-12-08. The A-polynomial from the noncommutative viewpoint. https://arxiv.org/abs/math/9812048

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