Related papers: Categorifications of the colored Jones polynomial

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…

We study the asymptotic expansion of the colored Jones polynomial (the Melvin-Morton expansion) using a recursion formula for the deframed universal weight system for the $sl(2)$ Lie algebra. Combined with the formula for the universal…

We establish a characterization of adequate knots in terms of the degree of their colored Jones polynomial. We show that, assuming the Strong Slope conjecture, our characterization can be reformulated in terms of "Jones slopes" of knots and…

We give a new definition of the Jones polynomial. Let L be an oriented knot or link obtained as the plat closure of a braid beta in B_{2n}. We define a covering space tilde{C} of the space of unordered n-tuples of distinct points in the…

The SL_3 colored Jones polynomial of the trefoil knot is a $q$-holonomic sequence of two variables with natural origin, namely quantum topology. The paper presents an explicit set of generators for the annihilator ideal of this…

We show examples of knots with the same polynomial invariants and hyperbolic volumes, with variously coinciding 2-cable polynomials and colored Jones polynomials, which are not mutants.

We continue our study of the degree of the colored Jones polynomial under knot cabling started in "Knot Cabling and the Degree of the Colored Jones Polynomial" (arXiv:1501.01574). Under certain hypothesis on this degree, we determine how…

This is an introduction to the Volume Conjecture and its generalizations for nonexperts. The Volume Conjecture states that a certain limit of the colored Jones polynomial of a knot would give the volume of its complement. If we deform the…

In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links. The invariant is initially be expressed in terms of a relative of the…

This paper defines versions of the Jones polynomial and Khovanov homology by using several maps from the set of Gauss diagrams to its variant. Through calculation of some examples, this paper also shows that these versions behave…

New invariants of links are constructed using the skein invariant polynomial of colored links defined by the author in [1]. These invariants are stronger than the homflypt polynomial.

We consider two well known constructions of link invariants. One uses skein theory: you resolve each crossing of the link as a linear combination of things that don't cross, until you eventually get a linear combination of links with no…

In this paper we give a quantum statistical interpretation for the bracket polynomial state sum <K> and for the Jones polynomial. We use this quantum mechanical interpretation to give a new quantum algorithm for computing the Jones…

We consider the potential function of the colored Jones polynomial for a link with arbitrary colors and obtain the cone-manifold structure for the link complement. In addition, we establish a relationship between a saddle point equation and…

This article provides an overview of relative strengths of polynomial invariants of knots and links, such as the Alexander, Jones, Homflypt, and Kaufman two-variable polynomial, Khovanov homology, factorizability of the polynomials, and…

We study the asymptotic behavior of the $N$-dimensional colored Jones polynomial evaluated at $\exp(\xi/N)$ for a real number $\xi$ greater than a certain constant. We prove that, from the asymptotic behavior, we can extract the…

For every n-component ribbon link L we prove that the Jones polynomial V(L) is divisible by the polynomial V(O^n) of the trivial link. This integrality property allows us to define a generalized determinant det V(L) := [V(L)/V(O^n)]_(t=-1),…

Biquandle brackets define invariants of classical and virtual knots and links using skein invariants of biquandle-colored knots and links. Biquandle coloring quivers categorify the biquandle counting invariant in the sense of defining…

We use categorical annular evaluation to give a uniform construction of both $\mathfrak{sl}_n$ and HOMFLYPT Khovanov-Rozansky link homology, as well as annular versions of these theories. Variations on our construction yield…

We extend the state models for Jones and Alexander polynomials of classical links to state models of 2-variable polynomials in the case of singular links. Moreover, we extend both of them to polynomials with d+1 variables for long singular…