THE COMPUTATION OF THE NON-COMMUTATIVE GENERALIZATION OF THE A-POLYNOMIAL OF THE FIGURE-EIGHT KNOT.

The paper computes the noncommutative A-ideal of the figure-eight knot, a noncommutative generalization of the A-polynomial. It is shown that if a knot has the same A-ideal as the figure-eight knot, then all colored Kauffman brackets are the same as those of the figure eight knot. [ABSTRACT FROM AUTHOR]