A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Method converts virtual link diagrams to normal form, preserving equivalence.
Method converts virtual link diagrams to normal ones.
Paper constructs cyclic coverings of virtual link diagrams, proving equivalence of certain maps.
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 span of the f-polynomial of an alternating virtual link L is determined by the nu…
Refines virtual link equality criterion for diagrams with one virtual crossing.
New coloring method limits moves needed between virtual-link diagrams.
A new index measures how many changes are needed to turn virtual links into simple ones.
By adding or removing appropriate structures to Gauss diagram, one can create useful objects related to virtual links. In this paper few objects of this kind are studied: twisted virtual links generalizing virtual links; signed chord diagrams staying halfway between twisted virtual links and Kauffman bracket / Khovanov…
We prove that a virtual link diagrams satisfying two conditions on the Khovanov homology is minimal, that is, there is no virtual diagram representing the same link with smaller number of crossings. This approach works for both classical and virtual links
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2-dimensional surface.) We prove that if a minimal genus …
The paper defines new representations and groups related to virtual links.
New tool lassos connects virtual and surface link diagrams, changing primeness rules.
The paper confirms a conjecture and extends arrow polynomial to twisted links.
Study links' flat-virtual diagrams to create link invariants.
Paper discusses a new link invariant from virtual link theory.
The paper classifies virtual links using the arc shift operation.
Paper proves link diagrams can be realized for some but not all types of links.
In 2002, D. Hrencecin and L.H. Kauffman defined a filamentation invariant on oriented chord diagrams that may determine whether the corresponding flat virtual knot diagrams are non-trivial. A virtual knot diagram is non-classical if its related flat virtual knot diagram is non-trivial. Hence filamentations can be used …
New link invariants derived from crossing multiplexing.
Paper discusses when virtual links are equivalent as twisted links.
New polynomial invariants for virtual links are stronger than F-polynomials.
We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also define generalizations of virtual link diagrams and Gauss codes to represent virtua…
Minimal crossing virtual links have minimal supporting genus.
Virtual index cocycles reformulate virtual link invariants.
Zh-construction links virtual links to classical ones, simplifying knot invariants.
A classical link in 3-space can be represented by a Gauss paragraph encoding a link diagram in a combinatorial way. A Gauss paragraph may code not a classical link diagram, but a diagram with virtual crossings. We present a criterion and a linear algorithm detecting whether a Gauss paragraph encodes a classical link. W…
Wirtinger number equals virtual bridge number for virtual links.
New invariant for virtual links defined using homology.
New HOMFLY-PT homology detects non-braidlike isotopies in link diagrams.
Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link. It is defined by considering the o…
We define a generalization of virtual links to arbitrary dimensions by extending the geometric definition due to Carter et al. We show that many homotopy type invariants for classical links extend to invariants of virtual links. We also define generalizations of virtual link diagrams and Gauss codes to represent virtua…
Paper introduces a new skein relation for multivariable polynomials of virtual links.
In the present paper we give a simple proof of the fact that the set of virtual links with orientable atoms is closed. More precisely, the theorem states that if two virtual diagrams and have orientable atoms and they are equivalent by Reidemeister moves, then there is a sequence of diagrams $K = K_1 \to...\to…
Virtual knots and links get multicrossings and petal diagrams.
We introduce two kinds of structures, called v-structures and t-structures, on biquandles. These structures are used for colorings of diagrams of virtual links and twisted links such that the numbers of colorings are invariants. Given a biquandle or a quandle, we give a method of constructing a biquandle with these str…
Dye and Kauffman defined surface bracket polynomials for virtual links by use of surface states, and found a relationship between the surface states and the minimal genus of a surface in which a virtual link diagram is realized. They and Miyazawa independently defined a multivariable polynomial invariant of virtual lin…
The article establishes a polynomial for signed cyclic graphs and links it to checkerboard colorability.
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kirby calculus. As a result, it is also an invariant of the 3-manifolds represented by the classical link diagrams. This generalization is used…
Two welded (respectively virtual) link diagrams are homotopic if one may be transformed into the other by a sequence of extended Reidemeister moves, classical Reidemeister moves, and self crossing changes. In this paper, we extend Milnor's mu and bar mu invariants to welded and virtual links. We conclude this paper wit…
New quantum invariants for 3-manifolds with boundary defined via virtual links.
Core groups are link invariants defined by arc or region presentations.
Every link diagram can be represented as a signed ribbon graph. However, different link diagrams can be represented by the same ribbon graphs. We determine how checkerboard colourable diagrams of links in real projective space, and virtual link diagrams, that are represented by the same ribbon graphs are related to eac…
In the present paper we bring together minimality conditions proposed in previous two papers and present some new minimality conditions for classical and virtual knots and links.
We introduce an equivalence relation, called stable equivalence, on knot diagrams and closed curves on surfaces. We give bijections between the set of abstract knots, the set of virtual knots, and the set of the stable equivalence classes of knot diagrams on surfaces. Using these bijections, we define concordance and l…
Study algebraic invariants of multi-virtual links.
Proves a theorem for surface links, simplifying diagrams of links.
New quantum invariants for 3-manifolds with boundary calculated.
This paper connects virtual biquandles to biquandles for virtual link colorings.