相关论文: An invariant for open virtual strings
We characterize, in an algebraic and in a diagrammatic way, Milnor string link invariants indexed by sequences where any index appears at most $k$ times, for any fixed $k\ge 1$. The algebraic characterization is given in terms of an…
Some issues in the loop variable renormalization group approach to gauge invariant equations for the free fields of the open string are discussed. It had been shown in an earlier paper that this leads to a simple form of the gauge…
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of…
We review recent work showing that there exists a large class of new stable black strings which are not translationally invariant. Both neutral and charged black strings are considered. The discussion includes known properties of these new…
In these notes we collect some results about finite dimensional representations of $U_q(\mathfrak{gl}(1|1))$ and related invariants of framed tangles which are well-known to experts but difficult to find in the literature. In particular, we…
A new set of boundary conditions for string propagators is proposed in this paper. The boundary conditions are parametrized by a complex number $\lambda$. Under these new boundary conditions, the left-moving and right-moving modes are…
We find that Alexander polynomial of a ribbon knot in $ \mathbb{Z}HS^3 $ is determined by the intrinsic singularity information of its ribbon, and give a formula to calculate Alexander polynomial of a ribbon knot by that. We define half…
Given a homomorphism from a knot group to a fixed group, we introduce an element of a $K_1$-group, which is a generalization of (twisted) Alexander polynomials. We compare this $K_1$-class with other Alexander polynomials. In terms of…
A perturbative expansion of knot invariants is derived using quantum cluster algebras. By interpreting the $R$-matrix of $U_q(\mathfrak{sl}_2)$ as a cluster transformation and introducing an auxiliary parameter $\epsilon$, we derive a…
The Levine-Tristram signature admits an n-variable extension for n-component links: it was first defined as an integer valued function on $(S^1\setminus\{1\})^n$, and recently extended to the full torus $T^n$. The aim of the present article…
A non-negative integer invariant, estimating from below the number of geometrically different critical points of a smooth function $f$ defined in the 2-disk, $f:\mathbb{B}^{2}\rightarrow\mathbb{R}$, is considered. (We denote it by…
In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind…
We consider an arbitrary representation of the additive group over a field of characteristic zero and give an explicit description of a finite separating set in the corresponding ring of invariants.
String attractors are a combinatorial tool coming from the field of data compression. It is a set of positions within a word which intersects an occurrence of every factor. While one-sided infinite words admitting a finite string attractor…
For a complex analytic variety with an action of a finite group and for an invariant 1-form on it, we give an equivariant version (with values in the Burnside ring of the group) of the local Euler obstruction of the 1-form and describe its…
Given a virtual knot $K$, we construct a group $VG_K$ called the virtual knot group, and we use the elementary ideals of $VG_K$ to define invariants of $K$ called the virtual Alexander invariants. For instance, associated to the $k=0$ ideal…
We extend an earlier proposal for a gauge invariant description of off-shell open strings (at tree level), using loop variables, to off-shell closed strings (at tree level). The basic idea is to describe the closed string amplitudes as a…
Construction of a universal finite-type invariant can be reduced, under suitable assumptions, to the solution of certain equations (the hexagon and pentagon equations) in a particular graded associative algebra of chord diagrams. An…
Modular invariance is a necessary condition for the consistency of any closed string theory. In particular, it imposes stringent constraints on the spectrum of orbifold theories, and in principle determines their spectrum uniquely up to…
Ribbon tangles are proper embeddings of tori and cylinders in the $4$-ball~$B^4$, "bounding" $3$-manifolds with only ribbon disks as singularities. We construct an Alexander invariant $\mathsf{A}$ of ribbon tangles equipped with a…