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 proves chainmail links are L-space links.
New examples of hyperbolic links with generalized torsion elements found.
We formalize networks with evolving structures as temporal networks and propose a generative link prediction model, Generative Link Sequence Modeling (GLSM), to predict future links for temporal networks. GLSM captures the temporal link formation patterns from the observed links with a sequence modeling framework and h…
Extends Goldberg's result for string links over surfaces.
A virtual link is a generalization of a classical link that is defined as an equivalence class of certain diagrams, called virtual link diagrams. It is further generalized to a twisted link. Twisted links are in one-to-one correspondence with stable equivalence classes of links in oriented thickenings of (possibly non-…
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…
New Arf invariants for colored links determined by linking numbers.
Study of generalized knots and links, proving inequality involving crossing number and braid index.
The paper characterizes links in 3D from divides with cusps.
It is shown that any handle-irreducible summand of every stable-ribbon surface-link is a unique ribbon surface-link up to equivalences, so that every stable-ribbon surface-link is a ribbon surface-link. This is a generalization of a previously observed result for a stably trivial surface-link. Two observations are give…
Augmented alternating links are links obtained by adding trivial components that bound twice-punctured disks to non-split reduced non-2-braid prime alternating projections. These links are known to be hyperbolic. Here, we extend to show that generalized augmented alternating links, which allow for new trivial component…
A handlebody-link is a disjoint union of embeddings of handlebodies in and an HL-homotopy is an equivalence relation on handlebody-links generated by self-crossing changes. The second author and Ryo Nikkuni classified the set of HL-homotopy classes of 2-component handlebody-links completely using the linking numb…
We generalized the periodic links to \emph{transitive} links in a -manifold . We find a complete classification theorem of transitive links in a -dimensional sphere . We study these links from several different aspects including polynomial invariants using the relation between link polynomials of…
Study of Lorenz links and T-links, showing equivalence and unique presentations.
Standard position for surfaces extended to weakly generalized alternating links.
The study examines obstructions to links being shake slice.
Two link diagrams are link homotopic if one can be transformed into the other by a sequence of Reidemeister moves and self crossing changes. Milnor introduced invariants under link homotopy called . Nanophrases, introduced by Turaev, generalize links. In this paper, we extend the notion of link homotopy to nanop…
The paper studies pseudo links in genus g handlebodies, generalizing knot theory.
Theory is developed for linear-quadratic at infinity generating families for Legendrian knots in R^3. It is shown that the unknot with maximal Thurston--Bennequin invariant of -1 has a unique linear-quadratic at infinity generating family, up to fiber-preserving diffeomorphism and stabilization. From this, invariant ge…
Habiro gave principal ideals of Z[q,q^{-1}] in which certain linear combinations of the colored Jones polynomials of algebraically-split links take values. The author proved that the same linear combinations for ribbon links, boundary links and Brunnian links are contained in smaller ideals of Z[q,q^{-1}] generated by …
New methods detect and create Brunnian links efficiently.
We introduce the notion of a ribbon-clasp surface-link, which is a generalization of a ribbon surface-link. We generalize the notion of a normal form on embedded surface-links to the case of immersed surface-links and prove that any (immersed) surface-link can be described in a normal form. It is known that an embedded…
A method to convert pretzel links into braids.
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…
Given a closed, oriented, connected 3-manifold, M, we define higher-order linking forms on the higher-order Alexander modules of M. These higher-order linking forms generalize similar linking forms for knots previously studied by the author, which were themselves generalizations of the classical Blanchfield linking for…
A theory of signatures for odd-dimensional links in rational homology spheres is studied via their generalized Seifert surfaces. The jump functions of signatures are shown invariant under appropriately generalized concordance and a special care is given to accommodate 1-dimensional links with mutual linking. Furthermor…
The paper studies pseudo and singular links in a solid torus, developing invariants and algebraic structures.
The paper explores orderability in link quandles and provides various results.
Paper conjectures Links-Gould invariant generalizes Alexander polynomial.
Classifies colored links and spatial graphs up to colored link-homotopy.
We prove a Kauffman-Murasugi-Thistlethwaite theorem for alternating links in thickened surfaces. It states that any reduced alternating diagram of a link in a thickened surface has minimal crossing number, and any two reduced alternating diagrams of the same link have the same writhe. This result is proved more general…
New findings on hyperbolicity of augmented links in thickened surfaces.
Traditionally introduced in terms of advanced topological constructions, many link invariants may also be defined in much simpler terms given their values on a few initial links and a recursive formula on a skein triangle. Then the crucial question to ask is how many initial values are necessary to completely determine…
Study of alternating links on nonorientable surfaces, extending results to nonorientable projections.
Investigates BNSR invariants of link and knot groups, proving specific properties.
This paper is a generalization of the author's previous work on link homotopy to link concordance. We show that the only real-valued finite type link concordance invariants are the linking numbers of the components.
Using computer calculations and working with representatives of pretzel tangles we established general adequacy criteria for different classes of knots and links. Based on adequate graphs obtained from all Kauffman states of an alternating link we defined a new numerical invariant: adequacy number, and computed adequac…
Paper connects homologically fibered links to solutions of equations.
We define and prove properties of link lattice complexes for plumbed links.
The paper studies hyperbolic geometry of links formed by adding trivial components to knots.
The twisting technique creates infinite links.
Study fully augmented links in thickened torus, generalizing results.
Extends Satoh's map to virtual m-links and constructs geometric pictures.
Geometrically describes the linear and quadratic forms for rational links.
The paper generalizes linking number properties for complete graphs.
Virtual knot theory is a generalization of knot theory which is based on Gauss chord diagrams and link diagrams on closed oriented surfaces. A twisted knot is a generalization of a virtual knot, which corresponds to a link diagram on a possibly non-orientable surface. In this paper, we discuss an invariant of twisted l…
New polynomial invariant distinguishes singular links.
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…