The noncommutative A-ideal of a (2,2p+1)-torus knot determines its Jones polynomial

2002/01/11 by Razvan Gelca, Răzvan Gelca, Gelca, Razvan +2
Computer Science · Mathematics · #57M27 #Advanced Combinatorial Mathematics #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M27 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0201100

15 pages, Latex, 13 figures

arxiv created 2002/01/11 · openalex publication_date 2002/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The noncommutative A-ideal of a knot is a generalization of the A-polynomial, defined using Kauffman bracket skein modules. In this paper we show that any knot that has the same noncommutative A-ideal as the (2,2p+1)-torus knot has the same colored Jones polynomials. This is a consequence of the orthogonality relation, which yields a recursive relation for computing all colored Jones polynomials of the knot.

Citations

• Invariants of 3-manifolds via link polynomials and quantum groups

Related

• The A-polynomial from the noncommutative viewpoint
• On the relation between the A-polynomial and the Jones polynomial
• The computation of the non-commutative generalization of the A-polynomial for the figure-eight knot
• The Colored Jones Polynomial and the A-Polynomial of Knots
• A recursive relation in the (2p+1,2) torus knot