DIFFERENCE AND DIFFERENTIAL EQUATIONS FOR THE COLORED JONES FUNCTION

DOI10.1142/S0218216508006245zbMath1155.57012arXivmath/0306229OpenAlexW2016278251MaRDI QIDQ3519640

Stavros Garoufalidis

Publication date: 19 August 2008

Published in: Journal of Knot Theory and Its Ramifications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0306229

zbMATH Keywords

loop expansionholonomic functionKauffman bracket skein modulecolored Jones function

Mathematics Subject Classification ID

Related Items (8)

The strong AJ conjecture for cables of torus knots ⋮ The colored Jones function is \(q\)-holonomic ⋮ The skein module of torus knots ⋮ Reconstructing WKB from topological recursion ⋮ Torus knot polynomials and Susy Wilson loops ⋮ The volume conjecture, perturbative knot invariants, and recursion relations for topological strings ⋮ The NoncommutativeA-Polynomial of (−2, 3,n) Pretzel Knots ⋮ Skein theory for \(SU(n)\)-quantum invariants

Cites Work

• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• The colored Jones polynomial and the \(A\)-polynomial of knots
• Hecke algebra representations of braid groups and link polynomials
• The Yang-Baxter equation and invariants of links
• A holonomic systems approach to special functions identities
• Galois theory of difference equations
• The universal \(R\)-matrix, Burau representation, and the Melvin-Morton expansion of the colored Jones polynomial
• Non-triviality of the \(A\)-polynomial for knots in \(S^3\)
• A rational noncommutative invariant of boundary links
• Complexity of stratifications of semi-Pfaffian sets
• The colored Jones function is \(q\)-holonomic
• Conditions which imply that subrings of semiprimary rings are semiprimary
• Structure of representations generated by vectors of highest weight
• 𝑆𝐿_{𝑛}-character varieties as spaces of graphs
• The A-polynomial from the noncommutative viewpoint
• On the relation between the A-polynomial and the Jones polynomial
• THE NONCOMMUTATIVE A-IDEAL OF A (2, 2p + 1)-TORUS KNOT DETERMINES ITS JONES POLYNOMIAL
• Skein modules and the noncommutative torus
• DIFFERENCE EQUATION OF THE COLORED JONES POLYNOMIAL FOR TORUS KNOT
• The colored Jones polynomials and the simplicial volume of a knot

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