The colored Jones polynomial and the \(A\)-polynomial of knots

DOI10.1016/j.aim.2006.01.006zbMath1114.57014arXivmath/0407521OpenAlexW2155883679MaRDI QIDQ855515

Le Ty Kuok Tkhang

Publication date: 7 December 2006

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407521

zbMATH Keywords

Jones polynomialKauffman bracket skein moduleAJ-conjectureA-polynomialtwo-bridge knots

Mathematics Subject Classification ID

Related Items (45)

Asymptotics of the colored Jones polynomial and the A-polynomial ⋮ The AJ-Conjecture and cabled knots over torus knots ⋮ Big data approaches to knot theory: Understanding the structure of the Jones polynomial ⋮ The strong AJ conjecture for cables of torus knots ⋮ The colored Jones function is \(q\)-holonomic ⋮ On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere ⋮ 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 \(7_{4}\) ⋮ The skein module of torus knots ⋮ The skein algebra of the Borromean rings complement ⋮ Quantum invariant congruence for periodic links ⋮ Representation variety of free or surface groups and Reidemeister torsion ⋮ The Kauffman bracket skein module of the complement of \((2, 2p + 1)\)-torus knots via braids ⋮ Adequate links in thickened surfaces and the generalized Tait conjectures ⋮ Quantized representations of knot groups ⋮ Proof of a stronger version of the AJ conjecture for torus knots ⋮ A diagrammatic approach to the AJ conjecture ⋮ The colored HOMFLYPT function is q-holonomic ⋮ DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION ⋮ QUANTUM TEICHMÜLLER SPACES AND QUANTUM TRACE MAP ⋮ Asymptotics of the colored Jones function of a knot ⋮ Confluence theory for graphs ⋮ The Kauffman bracket skein module of two-bridge links ⋮ Recurrence relations and asymptotics of colored Jones polynomials ⋮ The \(C\)-polynomial of a knot ⋮ On lassos and the Jones polynomial of satellite knots ⋮ Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function ⋮ On Kauffman bracket skein modules of marked 3-manifolds and the Chebyshev-Frobenius homomorphism ⋮ THE NON-COMMUTATIVE A-POLYNOMIAL OF TWIST KNOTS ⋮ The strong AJ conjecture for the figure 8 knot ⋮ Roger and Yang’s Kauffman bracket arc algebra is finitely generated ⋮ Double affine Hecke algebras and generalized Jones polynomials ⋮ On the skein module of the product of a surface and a circle ⋮ Quantum knot invariants ⋮ Character varieties ⋮ THE CHARACTER VARIETY OF A FAMILY OF ONE-RELATOR GROUPS ⋮ Experimental evidence for the Volume Conjecture for the simplest hyperbolic non-2-bridge knot ⋮ Infinite families of hyperbolic 3‐manifolds with finite‐dimensional skein modules ⋮ THE UNIVERSAL CHARACTER RING OF THE (-2, 2m + 1, 2n)-PRETZEL LINK ⋮ The AJ-conjecture and cabled knots over the figure eight knot ⋮ A Note on Representation Variety of Abelian Groups and Reidemeister Torsion ⋮ On Kauffman bracket skein modules at roots of unity ⋮ Nahm sums, stability and the colored Jones polynomial ⋮ Knot state asymptotics. I: AJ conjecture and abelian representations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Varieties of group representations and splittings of 3-manifolds
• 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
• The Kauffman bracket skein module of a twist knot exterior
• On skein algebras and \(Sl_2(\mathbb{C})\)-character varieties
• Representation theory and the \(A\)-polynomial of a knot
• Knots.
• The coloured Jones function
• On the Melvin-Morton-Rozansky conjecture
• The colored Jones function is \(q\)-holonomic
• The A-polynomial from the noncommutative viewpoint
• On the relation between the A-polynomial and the Jones polynomial
• A polynomial invariant for knots via von Neumann algebras
• Varieties of representations of finitely generated groups
• Skein modules and the noncommutative torus
• DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT
• COMMENSURABILITY CLASSES OF TWIST KNOTS
• THE (2, ∞)-SKEIN MODULE OF THE COMPLEMENT OF A (2, 2p+1) TORUS KNOT
• Quantum invariants of knots and 3-manifolds

This page was built for publication: The colored Jones polynomial and the \(A\)-polynomial of knots