Related papers: On virtual link invariants
The Homflypt and Kauffman skein modules of the projective space are computed. Both are free and generated by some infinite set of links. This set may be chosen to be L_n, where L_n is an arbitrary link consisting of n projective lines for…
Geometric interpretations of some virtual knot invariants are given in terms of invariants of links in $\mathbb{S}^3$. Alexander polynomials of almost classical knots are shown to be specializations of the multi-variable Alexander…
We present a new link invariant which depends on a representation of the link group in SO(3). The computer calculations indicate that an abelian version of this invariant is expressed in terms of the Alexander polynomial of the link. On the…
In order to study certain algebraic objects, and notably algebraic groups, Serre introduced the notion on invariants, in particular cohomological invariants. The construction of non-trivial cohomological invariants of algebraic groups is an…
We extend the Kamada-Miyazawa polynomial to virtual singular links, which is valued in $\mathbb{Z}[A^2, A^{-2}, h]$. The decomposition of the resulting polynomial into two components, one in $\mathbb{Z}[A^2, A^{-2}]$ and the other in…
We consider knot theories possessing a {\em parity}: each crossing is decreed {\em odd} or {\em even} according to some universal rule. If this rule satisfies some simple axioms concerning the behaviour under Reidemeister moves, this leads…
The forbidden moves in virtual knot theory can be used to unknot any knot, virtual or classical; however, multi-component crossings in links can still survive, resulting a fused link. Using the forbidden moves, we categorify fused links…
We show that a variation of Milnor's $\bar\mu$-invariants, the so-called Campbell-Hausdorff invariants introduced recently by Stefan Papadima, are of finite type with respect to {\it marked singular links}. These link invariants are…
A categorification of a polynomial link invariant is an homological invariant which contains the polynomial one as its graded Euler characteristic. This field has been initiated by Khovanov categorification of the Jones polynomial. Later,…
A weak chord index $Ind'$ is constructed for self crossing points of virtual links. Then a new writhe polynomial $W$ of virtual links is defined by using $Ind'$. $W$ is a generalization of writhe polynomial defined in [6]. Based on $W$,…
In the canonical quantization of gravity in terms of the Ashtekar variables one uses paths in the 3-space to construct the quantum states. Usually, one restricts oneself to families of paths admitting only finite number of isolated…
We use an action, of 2l-component string links on l-component string links, defined by the first author and Xiao-Song Lin, to lift the indeterminacy of finite type link invariants. The set of links up to this new indeterminacy is in…
In this paper we show how generalized quaternions, including 2X2 matrices, can be used to find solutions of a non-commuting equation intimately connected with braid groups. These solutions can then be used to find polynomial invariants of…
We introduce and study strongly invertible Legendrian links in the standard contact three-dimensional space. We establish the equivariant analogs of basic results separately well-known for strongly invertible and Legendrian links, i.e. the…
For an oriented virtual link, L.H. Kauffman defined the f-polynomial (Jones polynomial). The supporting genus of a virtual link diagram is the minimal genus of a surface in which the diagram can be embedded. In this paper we show that the…
Laplacian matrices of weighted graphs in surfaces $S$ are used to define module and polynomial invariants of $Z/2$-homologically trivial links in $S \times [0,1]$. Information about virtual genus is obtained.
Real-world road networks have an approximate scale-invariance property; can one devise mathematical models of random networks whose distributions are {\em exactly} invariant under Euclidean scaling? This requires working in the continuum…
We introduce a variant of the $K$-theoretic quantized Coulomb branch constructed by Braverman--Finkelberg--Nakajima, by application of a new virtual intersection theory. In the abelian case, we define Verma modules for such virtual Coulomb…
In this article we construct link invariants and 3-manifold invariants from the quantum group associated with Lie superalgebra $\mathfrak{sl}(2|1)$. This construction based on nilpotent irreducible finite dimensional representations of…
It is known that the Kauffman-Murasugi-Thislethwaite type inequality becomes an equality for any (possibly virtual) adequate link diagram. We refine this condition. As an application we obtain a criterion for virtual link diagram with…