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

RĂZVAN GELCA

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

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and

JEREMY SAIN

Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA

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https://doi.org/10.1142/S0218216504003482Cited by:6 (Source: Crossref)

Abstract

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.

Keywords:

AMSC: 57M27

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