The coloured Jones function

DOI10.1007/BF02099310zbMath0845.57007OpenAlexW1997065775MaRDI QIDQ1894871

Paul M. Melvin, Hugh R. Morton

Publication date: 22 September 1996

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02099310

zbMATH Keywords

invariants\(R\)-matrixVassiliev invariantframed knot

Mathematics Subject Classification ID

Related Items (45)

Cabled Wilson loops in BF theories ⋮ Branches, quivers, and ideals for knot complements ⋮ Higher order terms in the Melvin-Morton expansion of the colored Jones polynomial ⋮ Universal weight systems and the Melvin-Morton expansion of the colored Jones knot invariant ⋮ The colored Jones polynomial and the \(A\)-polynomial of knots ⋮ ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT ⋮ ON THE ANALYTIC PROPERTIES OF THE z-COLOURED JONES POLYNOMIAL ⋮ A non-commutative formula for the colored Jones function ⋮ A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. I ⋮ A contribution of the trivial connection of the Jones polynomial and Witten's invariant of 3d manifolds. II ⋮ Revisiting the Melvin-Morton-Rozansky expansion, or there and back again ⋮ A graphical approach to the Melvin-Morton conjecture. I ⋮ The universal \(R\)-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial ⋮ Higher rank \(\hat{Z}\) and \(F_K\) ⋮ 𝑈_{𝑞}(𝑠𝑙(2))-quantum invariants from an intersection of two Lagrangians in a symmetric power of a surface ⋮ A non-commutative Reidemeister-Turaev torsion of homology cylinders ⋮ A cable knot and BPS-series ⋮ The 3-loop polynomial of knots obtained by plumbing the doubles of two knots ⋮ A unified quantum \(SO(3)\) invariant for rational homology 3-spheres ⋮ BPS invariants for a knot in Seifert manifolds ⋮ Genus expansion of HOMFLY polynomials ⋮ Knot complement, ADO invariants and their deformations for torus knots ⋮ On \(p\)-adic convergence of perturbative invariants of some rational homology spheres ⋮ FEYNMAN LOOPS AND THREE-DIMENSIONAL QUANTUM GRAVITY ⋮ On the colored Jones polynomial and the Kashaev invariant ⋮ A unified Witten-Reshetikhin-Turaev invariant for integral homology spheres ⋮ Quivers for 3-manifolds: the correspondence, BPS states, and 3d \(\mathcal{N} = 2\) theories ⋮ DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT ⋮ The volume conjecture, perturbative knot invariants, and recursion relations for topological strings ⋮ The colored Jones polynomials and the simplicial volume of a knot ⋮ A cabling formula for the 2-loop polynomial of knots ⋮ Hidden structures of knot invariants ⋮ OHTSUKI INVARIANTS FOR INTEGRAL HOMOLOGY SPHERES AND HABIRO'S CYCLOTOMIC EXPANSION ⋮ On knots, complements, and \(6j\)-symbols ⋮ A two-variable series for knot complements ⋮ Large color R-matrix for knot complements and strange identities ⋮ On Ohtsuki's invariants of integral homology 3-spheres ⋮ Topological formula of the loop expansion of the colored Jones polynomials ⋮ AN L²-ALEXANDER INVARIANT FOR KNOTS ⋮ ON HABIRO'S CYCLOTOMIC EXPANSIONS OF THE OHTSUKI INVARIANT ⋮ A lower bound for the number of Vassiliev knot invariants ⋮ Three-dimensional quantum gravity, Chern-Simons theory, and the \(A\)-polynomial ⋮ IS THE JONES POLYNOMIAL OF A KNOT REALLY A POLYNOMIAL? ⋮ \({\widehat{Z}}\) at large \(N\): from curve counts to quantum modularity ⋮ Wheels, wheeling, and the Kontsevich integral of the unknot

Cites Work

• Quantum field theory and the Jones polynomial
• The 3-manifold invariants of Witten and Reshetikhin-Turaev for sl\((2,\mathbb{C})\)
• Perturbative expansion of Chern-Simons theory with non-compact Gauge group
• On the Vassiliev knot invariants
• Ribbon graphs and their invariants derived from quantum groups
• Invariants of 3-manifolds via link polynomials and quantum groups
• Knot polynomials and Vassiliev's invariants
• GAUSS CODES, QUANTUM GROUPS AND RIBBON HOPF ALGEBRAS
• The coloured Jones function and Alexander polynomial for torus knots
• Weights of Feynman diagrams, link polynomials and Vassiliev knot invariants

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