On the relation between the A-polynomial and the Jones polynomial

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Abstract

This paper shows that the noncommutative generalization of the A-polynomial of a knot, defined using Kauffman bracket skein modules, together with finitely many colored Jones polynomials, determines the remaining colored Jones polynomials of the knot. It also shows that under certain conditions, satisfied for example by the unknot and the trefoil knot, the noncommutative generalization of the A-polynomial determines all colored Jones polynomials of the knot.

Original languageEnglish
Pages (from-to)1235-1241
Number of pages7
JournalProceedings of the American Mathematical Society
Volume130
Issue number4
DOIs
StatePublished - 2002

Keywords

  • A-polynomial
  • Jones polynomial
  • Kauffman bracket
  • Noncommutative geometry

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