The coloured Jones function and Alexander polynomial for torus knots

DOI10.1017/S0305004100072959zbMath0852.57007OpenAlexW2045817582MaRDI QIDQ4697493

Hugh R. Morton

Publication date: 5 December 1996

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

Full work available at URL: https://doi.org/10.1017/s0305004100072959

zbMATH Keywords

Alexander polynomialquantum invarianttorus knotJones polynomialsframed knotcoloured Jones function

Mathematics Subject Classification ID

Related Items (39)

Holomorphic blocks in three dimensions ⋮ On \(q\)-series for principal characters of standard \(A_2^{( 2 )}\)-modules ⋮ Torus knots and quantum modular forms ⋮ The AJ-Conjecture and cabled knots over torus knots ⋮ Turaev-Viro invariants, colored Jones polynomials, and volume ⋮ The coloured Jones function ⋮ 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 ⋮ ASYMPTOTIC BEHAVIORS OF THE COLORED JONES POLYNOMIALS OF A TORUS KNOT ⋮ Volume Conjecture and Asymptotic Expansion ofq-Series ⋮ A contribution of the trivial connection to the Jones polynomial and Witten's invariant of 3d manifolds. I ⋮ Knots with Hopf crossing number at most one ⋮ Turaev–Viro invariants and cabling operations ⋮ The slope conjecture for graph knots ⋮ Proof of a stronger version of the AJ conjecture for torus knots ⋮ Torus knot and minimal model ⋮ Quantum invariants of three-manifolds obtained by surgeries along torus knots ⋮ DAHA approach to iterated torus links ⋮ The strong slope conjecture for twisted generalized Whitehead doubles ⋮ The colored Jones polynomial, the Chern-Simons invariant, and the Reidemeister torsion of a twice-iterated torus knot ⋮ A 𝑞-series identity via the 𝔰𝔩₃ colored Jones polynomials for the (2,2𝔪)-torus link ⋮ Proof of the volume conjecture for Whitehead doubles of a family of torus knots ⋮ DAHA and plane curve singularities ⋮ 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 ⋮ COLORED JONES POLYNOMIALS WITH POLYNOMIAL GROWTH ⋮ OHTSUKI INVARIANTS FOR INTEGRAL HOMOLOGY SPHERES AND HABIRO'S CYCLOTOMIC EXPANSION ⋮ Witten-Reshetikhin-Turaev function for a knot in Seifert manifolds ⋮ A two-variable series for knot complements ⋮ The strong slope conjecture for cablings and connected sums ⋮ On Ohtsuki's invariants of integral homology 3-spheres ⋮ Growth of Turaev–Viro invariants and cabling ⋮ The 𝑆𝐿₃ colored Jones polynomial of the trefoil ⋮ DAHA and skein algebra of surfaces: double-torus knots ⋮ The AJ-conjecture and cabled knots over the figure eight knot ⋮ Coloured \(\mathfrak{sl}_r\) invariants of torus knots and characters of \(\mathcal{W}_r\) algebras ⋮ Knot state asymptotics. I: AJ conjecture and abelian representations ⋮ Knots and signal transmission in topological quantum devices

Cites Work

• Ribbon graphs and their invariants derived from quantum groups
• ON THE INVARIANTS OF TORUS KNOTS DERIVED FROM QUANTUM GROUPS

This page was built for publication: The coloured Jones function and Alexander polynomial for torus knots