相关论文: The colored Jones function is q-holonomic

We extend the definition of the colored Jones polynomials to framed links and trivalent graphs in S^3 # k S^2 X S^1 using a state-sum formulation based on Turaev's shadows. Then, we prove that the natural extension of the Volume Conjecture…

To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose $n$th term is the $n$th colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the $n$th colored Jones polynomial at…

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones…

The Slope Conjecture relates a quantum knot invariant, (the degree of the colored Jones polynomial of a knot) with a classical one (boundary slopes of incompressible surfaces in the knot complement). The degree of the colored Jones…

We employ the sl(2) foam cohomology to define a cohomology theory for oriented framed tangles whose components are labelled by irreducible representations of U_q(sl(2)). We show that the corresponding colored invariants of tangles can be…

A function that is analytic on a domain of $\mathbb{C}^n$ is holonomic if it is the solution to a holonomic system of linear homogeneous differential equations with polynomial coefficients. We define and study the Bernstein-Sato polynomial…

In this paper we prove that the family of colored Jones polynomials of a knot in $S^3$ determines the family of ADO polynomials of this knot. More precisely, we construct a two variables knot invariant unifying both the ADO and the colored…

In this note we define a polynomial invariant for colored links by a skein relation. It specializes to the Jones polynomial for classical links.

A generalization of the volume conjecture relates the asymptotic behavior of the colored Jones polynomial of a knot to the Chern--Simons invariant and the Reidemeister torsion of the knot complement associated with a representation of the…

The extreme degrees of the colored Jones polynomial of any link are bounded in terms of concrete data from any link diagram. It is known that these bounds are sharp for semi-adequate diagrams. One of the goals of this paper is to show the…

Necessary and sufficient conditions are obtained under which the numerator of the partial derivative of a rational function holomorphic in open upper poly-halfplane is the sum of squares of polynomials.

We use the relation between the quantum su(2) R-matrix and the Burau representation of the braid group in order to study the structure of the colored Jones polynomial of links. We show that similarly to the case of a knot, the colored Jones…

Our goal is to compute the minimal-order recurrence of the colored Jones polynomial of the 7_4 knot, as well as for the first four double twist knots. As a corollary, we verify the AJ Conjecture for the simplest knot 7_4 with reducible…

In 1992, Wilf and Zeilberger conjectured that a hypergeometric term in several discrete and continuous variables is holonomic if and only if it is proper. Strictly speaking the conjecture does not hold, but it is true when reformulated…

In this article the discovery of the Jones Polynomial will be discussed, emphasizing the way in which it illustrated the remarkable unity between distinct parts of Mathematics, each with its own language, but initially without a dictionary.

Using the vertex model approach for braid representations, we compute polynomials for spin-1 placed on hyperbolic knots up to 15 crossings. These polynomials are referred to as 3-colored Jones polynomials or adjoint Jones polynomials.…

Steingrimsson (2001) showed that the chromatic polynomial of a graph is the Hilbert function of a relative Stanley-Reisner ideal. We approach this result from the point of view of Ehrhart theory and give a sufficient criterion for when the…

The colored Jones polynomial $J_{K,N}$ is an important quantum knot invariant in low-dimensional topology. In his seminal paper on quantum modular forms, Zagier predicted the behavior of $J_{K,0}(e^{2 \pi i x})$ under the action of…

Using the Huynh and Le quantum determinant description of the colored Jones polynomial, we construct a new combinatorial description of the colored Jones polynomial in terms of walks along a braid. We then use this description to show that…

Let $(M,\omega)$ be a Kahler manifold. An integrable function on M is called $\omega^q$-plurisubharmonic if it is subharmonic on all q-dimensional complex subvarieties. We prove that a smooth $\omega^q$-plurisubharmonic function is…