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

DOI10.1090/S0002-9939-01-06157-3zbMath0994.57014arXivmath/0004158OpenAlexW1708330518MaRDI QIDQ2781276

Razvan Gelca

Publication date: 19 March 2002

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0004158

zbMATH Keywords

noncommutative geometryKauffman bracketKauffman skein module

Mathematics Subject Classification ID

Related Items (28)

Asymptotics of the colored Jones polynomial and the A-polynomial ⋮ 4d quantum geometry from 3d supersymmetric gauge theory and holomorphic block ⋮ Sequencing BPS spectra ⋮ On skew tau-functions in higher spin theory ⋮ Colored HOMFLY polynomials for the pretzel knots and links ⋮ The colored Jones polynomial and the \(A\)-polynomial of knots ⋮ ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT ⋮ The universal character ring of some families of one-relator groups ⋮ The action of the Kauffman bracket skein algebra of the torus on the Kauffman bracket skein module of the 3-twist knot complement ⋮ Irreducibility of \(q\)-difference operators and the knot \(7_{4}\) ⋮ Kauffman bracket versus Jones polynomial skein modules ⋮ Representation variety of free or surface groups and Reidemeister torsion ⋮ Proof of a stronger version of the AJ conjecture for torus knots ⋮ DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION ⋮ COMPUTING THE A-POLYNOMIAL USING NONCOMMUTATIVE METHODS ⋮ The Kauffman bracket skein module of two-bridge links ⋮ THE COMPUTATION OF THE NON-COMMUTATIVE GENERALIZATION OF THE A-POLYNOMIAL OF THE FIGURE-EIGHT KNOT ⋮ Algebra of quantum \(\mathcal{C} \)-polynomials ⋮ The NoncommutativeA-Polynomial of (−2, 3,n) Pretzel Knots ⋮ THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS ⋮ Varieties via a filtration of the KBSM and knot contact homology ⋮ Quantum knot invariants ⋮ Character varieties ⋮ SOME RESULTS ABOUT THE KAUFFMAN BRACKET SKEIN MODULE OF THE TWIST KNOT EXTERIOR ⋮ Skein theory for \(SU(n)\)-quantum invariants ⋮ Infinite families of hyperbolic 3‐manifolds with finite‐dimensional skein modules ⋮ THE UNIVERSAL CHARACTER RING OF THE (-2, 2m + 1, 2n)-PRETZEL LINK ⋮ A Note on Representation Variety of Abelian Groups and Reidemeister Torsion

Cites Work

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• State models and the Jones polynomial
• Plane curves associated to character varieties of 3-manifolds
• Rings of \(SL_2(\mathbb{C})\)-characters and the Kauffman bracket skein module
• Topological quantum field theories derived from the Kauffman bracket
• Invariants of 3-manifolds via link polynomials and quantum groups
• The A-polynomial from the noncommutative viewpoint
• A polynomial invariant for knots via von Neumann algebras
• THE (2, ∞)-SKEIN MODULE OF LENS SPACES: A GENERALIZATION OF THE JONES POLYNOMIAL
• THE SKEIN METHOD FOR THREE-MANIFOLD INVARIANTS
• Skein modules and the noncommutative torus
• Non-commutative trigonometry and the A-polynomial of the trefoil knot
• Quantum invariants of knots and 3-manifolds

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