Related papers: $C_{n}$-moves and the difference of Jones polynomi…

For any virtual link $L = S \cup T$ that may be decomposed into a pair of oriented $n$-tangles $S$ and $T$, an oriented local move of type $T \mapsto T'$ is a replacement of $T$ with the $n$-tangle $T'$ in a way that preserves the…

We calculate Jones polynomials $V_L(t)$ for several families of alternating knots and links by computing the Tutte polynomials $T(G,x,y)$ for the associated graphs $G$ and then obtaining $V_L(t)$ as a special case of the Tutte polynomial.…

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),…

We compute the Jones polynomial for a three-parameter family of links, the twisted torus links of the form $T((p,q),(2,s))$ where $p$ and $q$ are coprime and $s$ is nonzero. When $s = 2n$, these links are the twisted torus knots…

We calculate Jones polynomials $V(H_r,t)$ for a family of alternating knots and links $H_r$ with arbitrarily many crossings $r$, by computing the Tutte polynomials $T(G_+(H_r),x,y)$ for the associated graphs $G_+(H_r)$ and evaluating these…

The colored $\mathfrak{sl}_{3}$ Jones polynomial $J_{(n_{1}, n_{2})}^{\mathfrak{sl}_{3}}(L;q)$ are given by a link and an $(n_{1}, n_{2})$-irreducible representation of $\mathfrak{sl}_{3}$. In general, it is hard to calculate $J_{(n_{1},…

We present a new 2-variable generalization of the Jones polynomial that can be defined through the skein relation of the Jones polynomial. The well-definedness of this new generalization is proved both algebraically and diagrammatically as…

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…

The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homology theory for unoriented virtual links. The graded Euler…

Khovanov homology is a recently introduced invariant of oriented links in $\mathbb{R}^3$. It categorifies the Jones polynomial in the sense that the (graded) Euler characteristic of the Khovanov homology is a version of the Jones polynomial…

We propose a new method for numerical calculation of link plynomials for knots given in 3 dimensions. We calculate derivatives of the Jones polynomial in a computational time proportional to $N^{\alpha}$ with respect to the system size $N$…

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 braid-like isotopy for links in 3-space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its corresponding Khovanov homology which are, in general, only…

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…

In [Duke Math. J. 101 (1999) 359-426], Mikhail Khovanov constructed a homology theory for oriented links, whose graded Euler characteristic is the Jones polynomial. He also explained how every link cobordism between two links induces a…

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is…

We give characterizations of the skein polynomial for links (as well as Jones and Alexander-Conway polynomials derivable from it), avoiding the usual "smoothing of a crossing" move. As by-products we have characterizations of these…

J.P. Levine showed that the Conway polynomial of a link is a product of two factors: one is the Conway polynomial of a knot which is obtained from the link by banding together the components; and the other is determined by the…

The purpose of this paper is to present a certain combinatorial method of constructing invariants of isotopy classes of oriented tame links. This arises as a generalization of the known polynomial invariants of Conway and Jones. These…

A polynomial invariant of virtual links, arising from an invariant of links in thickened surfaces introduced by Jaeger, Kauffman, and Saleur, is defined and its properties are investigated. Examples are given that the invariant can detect…