arXiv research

Study virtual fundamental classes of derived manifolds, proving invariant vanishes.

Continues work on derived manifolds and symplectic schemes, constructing virtual classes.

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equati…

Alternative definition of Casson invariants using virtual counting.

For a nonconstant holomorphic map between projective Riemann surfaces with conformal metrics, we consider invariant Schwarzian derivatives and projective Schwarzian derivatives of general virtual order. We show that these two quantities are related by the "Schwarzian derivative" of the metrics of the surfaces (at least…

Let $({\bf X},ω_{\bf X}^*)$ be a separated, $-2$-shifted symplectic derived $\mathbb C$-scheme, in the sense of Pantev, Toen, Vezzosi and Vaquie arXiv:1111.3209, of complex virtual dimension ${\rm vdim}_{\mathbb C}{\bf X}=n\in\mathbb Z$, and $X_{\rm an}$ the underlying complex analytic topological space. We prove that …

In this short note we show how virtual arbitrage opportunities can be modelled and included in the standard derivative pricing without changing the general framework.

ROCS-derived features enhance virtual screening performance.

A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidem…

We introduce an algebraic structure we call semiquandles whose axioms are derived from flat Reidemeister moves. Finite semiquandles have associated counting invariants and enhanced invariants defined for flat virtual knots and links. We also introduce singular semiquandles and virtual singular semiquandles which define…

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 is a polynomial $H_K(s,t,q)$ in three variables which we call the virtual Alexa…

New link invariants derived from crossing multiplexing.

The paper characterizes crystallographic groups derived from virtual braid and twin groups.

New bounds on virtual Rasmussen invariant derived from classical knot invariants.

Paper discusses a new link invariant from virtual link theory.

This paper describes a polynomial invariant of virtual knots that is defined in terms of an integer labeling of the virtual knot diagram. This labeling is seen to derive from an essentially unique structure of affine flat biquandle for flat virtual diagrams. The invariant is discussed in detail with many examples,inclu…

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 chirality and even non-invertibility of virtual knots and links. Furthermore, it …

Study on singular twisted links and virtual braids, extending knot theory concepts.

We generalize the Arbitrage Pricing Theory (APT) to include the contribution of virtual arbitrage opportunities. We model the arbitrage return by a stochastic process. The latter is incorporated in the APT framework to calculate the correction to the APT due to the virtual arbitrage opportunities. The resulting relatio…

It is an open question whether there are Vassiliev invariants that can distinguish an oriented knot from its inverse, i.e., the knot with the opposite orientation. In this article, an example is given for a first order Vassiliev invariant that takes different values on a virtual knot and its inverse. The Vassiliev inva…

This paper connects virtual biquandles to biquandles for virtual link colorings.

New polynomial invariants defined for long virtual knots.

The virtual Betti number conjecture states that any hyperbolic three-manifold has a finite cover with positive first Betti number. We show that this would follow if it were known that the derived series of the fundamental group $G$ of a hyperbolic three-manifold satisfies a certain stability property. The stability pro…

Paper defines doodles on closed surfaces, unifying classical and virtual theories.

The derived group of a permutation representation, introduced by R.H. Crowell, unites many notions of knot theory. We survey Crowell's construction, and offer new applications. The twisted Alexander group of a knot is defined. Using it, we obtain twisted Alexander modules and polynomials. Also, we extend a well-known t…

Study of commutator subgroups and crystallographic quotients of virtual groups.

This study simplifies verification of invariants in oriented virtual knots.

Two new polynomial invariants for long virtual knots.

The paper introduces derivations for quandles and their properties.

Study uses sentiment analysis to predict cryptocurrency token returns in virtual reality.

KANEL combines models for early hit enrichment in virtual screening.

Joyce has shown that the fundamental quandle of a classical knot can be derived from consideration of the fundamental group and the peripheral structure of the knot, and also that the group and much of the peripheral structure can be recovered from the quandle. We generalize these results to arbitrary dimensions, and a…

The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordisms which directly applies to classical knot and classical knot cobordisms. To do so, we give an alternate formulation for the Manturov defi…

Zh-construction links virtual links to classical ones, simplifying knot invariants.

A method to reduce boundary over-exploration in Bayesian optimization.

We define a group-valued invariant of virtual knots and relate it to various other group-valued invariants of virtual knots, including the extended group of Silver-Williams and the quandle group of Manturov and Bardakov-Bellingeri. A virtual knot is called almost classical if it admits a diagram with an Alexander numbe…

The Jones polynomial's divisibility is analyzed via local moves on virtual links.

New knot invariants derived from biquandle quivers.

Derived differential manifolds are constructed using the usual homotopy theory of simplicial rings of smooth functions. They are proved to be equivalent to derived differential manifolds of finite type, constructed using homotopy sheaves of homotopy rings (D.Spivak), thus preserving the classical cobordism ring. This r…

This paper establishes a correspondence between biquandle and quandle colorings for classical and surface links.

New knot invariants derived from non-abelian Yang-Baxter solutions.

Optimizes resource allocation for virtualized network functions based on performance profiles.

Proves a generalized vanishing theorem for quasi-smooth stacks, with applications in K-theory and birational geometry.

New virtualized Δ-move simplifies virtual knots and links.

Virtual index cocycles reformulate virtual link invariants.

The paper studies strict equivalence in multi-virtual linkoids with new invariants.

Researchers extend Alexander polynomial to knotoids and linkoids.

Paper constructs a new approach to extract Affine Index Polynomial from Sawollek Polynomial.