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.
Study links' flat-virtual diagrams to create link invariants.
Flat fully augmented links with homeomorphic complements are equivalent.
Every link is shown to be presentable as a boundary of an unknotted flat banded surface. A (flat) banded link is defined as a boundary of an unknotted (flat) banded surface. A link's (flat) band index is defined as the minimum number of bands required to present the link as boundaries of an unknotted (flat) banded surf…
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers or less using a special presentation of the flat plumbing basket surfaces. We find a complete classification theorem of links of the fla…
A flat plumbing basket is a surface consisting a disk and finitely many bands which are contained in distinct pages of the trivial open book decomposition of . In this paper, we construct a Legendrian link from a flat plumbing basket, and we describe a relation among the self-linking number, the Thursto…
We define the basket number, the flat plumbing number and the flat plumbing basket number of a link. Then we provide some upperbounds for these plumbing numbers by using Seifert's algorithm. We study the relation between these plumbing numbers and the genera of links.
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. These flat plumbing basket surface can be presented by a sequential presentation known as flat plumbing basket code first found by Furihata, Hirasawa and Kobayashi. The minimum number of flat plumbings to obtain…
The existence of basket, flat plumbing and flat plumbing basket surfaces of a link was first proven from a braid representative of the link. In the present article, we show the existence of such surfaces from an induced graph of the link. Consequently, we define the basket number, flat plumbing number and flat plumbing…
Study proves chainmail links are L-space links.
New proof shows no flat embedding for Petersen family graphs.
The paper connects link symmetries to finite subgroups of O(3).
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…
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 this probabilistic interpretation we introduce the notion of virtual flat biqua…
The paper introduces a semiquandle for flat virtual knots and connects it to u-polynomials.
A flat plumbing basket is a Seifert surface consisting of a disk and bands contained in distinct pages of the disk open book decomposition of the 3-sphere. In this paper, we examine close connections between flat plumbing baskets and the contact structure supported by the open book. As an application we give lower boun…
New polynomial invariants for virtual links are stronger than F-polynomials.
We extend the methods of Davis-Januszkiewicz-Lafont to provide a new obstruction to smooth Riemannian metric with non-positive sectional curvature. We construct examples of locally CAT(0) 4-manifolds , whose universal covers satisfy isolated flats condition and contain 2-dimensional flats with the property that $\sq…
This paper gives a polynomial invariant for flat virtual links. In the case of one component, the polynomial specializes to Turaev's virtual string polynomial. We show that Turaev's polynomial has the property that it is non-zero precisely when there is no filamentation of the knot, as described by Hrencecin and Kauffm…
Minkowski space is the local model of 3 dimensionnal flat spacetimes. Recent progress in the description of globally hyperbolic flat spacetimes showed strong link between Lorentzian geometry and Teichm{ü}ller space. We notice that Lorentzian generalisations of conical singularities are useful for the endeavours of desc…
The flat plumbing basket presentation of a link is introduced by Furihata, Hirasawa and Kobayashi. In this paper, we show that the pass-equivalence and an equivalence introduced by using the flat plumbing basket presentation are the same relation. Furthermore, we obtain an evaluation of the minimal number of bands used…
Identifies a mod- triple cup product for rational homology 3-spheres with specific first homology.
Curved flats linked to pairs of Lie applicable surfaces.
Combines higher complex structures with flat connections to link to -algebras.
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 …
Study minimum ribbonlength of immersed flat knots and links.
We show that if a link L with non-zero Alexander polynomial admits a locally flat cobordism to a `weakly m-split link', then the cobordism must have genus at least (m-1)/2. This generalises a recent result of J. Pardon.
Counterexample disproves conjecture on flat metrics and fiber bundles.
The paper defines a new invariant for links and uses it to show non-sliceness.
A graph G is intrinsically S^1-linked if for every embedding of the vertices of G into S^1, vertices that form the endpoints of two disjoint edges in G form a non-split link in the embedding. We show that a graph is intrinsically S^1-linked if and only if it is not outer-planar. A graph is outer-flat if it can be embed…
Study shows surgeries on specific links result in L-spaces.
Flat semigroups can represent normal weighted homogeneous surface singularities.
New formulas for spatial 2-bouquet graphs discovered.
New bounds link flat minima to good generalisation in overparameterized models.
We construct two knot invariants. The first knot invariant is a sum constructed using linking numbers. The second is an invariant of flat knots and is a formal sum of flat knots obtained by smoothing pairs of crossings. This invariant can be used in conjunction with other flat invariants, forming a family of invariants…
A weak chord index is constructed for self crossing points of virtual links. Then a new writhe polynomial of virtual links is defined by using . is a generalization of writhe polynomial defined in [6]. Based on , three invariants of virtual links are constructed. These invariants can be used to …
New research challenges the flatness-generalization link in deep neural networks.
We will discuss a method for visual presentation of knotted surfaces in the four space, by examining a number and a position of its Morse's critical points. Using this method, we will investigate surface-knot with one critical point of index 1. Then we show infinitely many mutually distinct surface-knots that has an em…
3D Schoenflies theorem for simply-connected 2-complexes.
We consider the group of unrestricted virtual braids, describe its structure and explore its relations with fused links. Also, we define the groups of flat virtual braids and virtual Gauss braids and study some of their properties, in particular their linearity.
The paper links set cuspidality to function regularity and flatness.
Given a closed Riemannian manifold and a pair of multi-curves in it, we give a formula relating the linking number of the later to the spectral theory of the Laplace operator acting on differential one forms. As an application, we compute the linking number of any two multi-geodesics of the flat torus of dimension 3, g…
Unified view of integrable systems linking CMC, isothermic, and Willmore surfaces.
The study extends Tutte's conflict graph concept to nonplanar graphs.
Kahler toric manifolds linked to dually flat spaces via affine isometry.
Bi-flat F-structures link to differential bicomplexes and Gauss-Manin connections.
This is a continuation of our previous paper [14]. In [14], we introduced the first Aeppli-Chern class on compact complex manifolds, and proved that the curvature form of the Levi-Civita connection represents the first Aeppli-Chern class which is a natural link between Riemannian geometry and complex geometry. …
We define a notion of concordance based on Euler characteristic, and show that it gives rise to a concordance group of links in the three-sphere, which has the concordance group of knots as a direct summand with infinitely generated complement. We consider variants of this using oriented and nonoriented surfaces as wel…
We introduce a new standard form of a Seifert surface . In that standard form, is obtained by successively plumbing flat annuli to a disk , where the gluing regions are all in . We show that any link has a Seifert surface in the standard form, and thereby present a new way of coding a link. We present an a…