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.
Enhanced bikei modules distinguish unoriented and non-orientable surface-links.
New singquandles help distinguish certain types of links.
Study on oriented disingquandles for distinguishing singular links.
Medial quandles fail to distinguish certain links, highlighting their limitations.
New polynomial invariant distinguishes singular links.
It is known that the first two-variable Links--Gould quantum link invariant is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations o…
Alexander quandles fail to distinguish certain links, thus not detecting causality.
New groups from virtual link stacks distinguish Kishino knots.
Paper provides a condition to distinguish links up to 4-moves.
The paper evaluates homology for links in a solid torus with special boundary conditions.
Introduces entropic tribrackets and their applications in link distinguishing.
We submit a new way to detect pairs of non-cobordant surface-links. We find a new example of a pair of non-cobordant surface-links with the following properties: Orr invariant, Cochran sequence, Sato-Levine invariant, the alinking number and one of Stallings's theorems cannot distinguish them. However our new way can d…
We derive formulas for HOMFLY polynomials of torus links using braid groups and linear recurrences.
New invariant distinguishes singular knots and links.
It is shown that, in the 1-jet space of the circle, the swapping and the flyping procedures, which produce topologically equivalent links, can produce nonequivalent legendrian links. Each component of the links considered is legendrian isotopic to the 1-jet of the 0-function, and thus cannot be distinguished by the cla…
Let be a positive integer. M. K. Dabkowski and J. H. Przytycki introduced the th Burnside group of links which is preserved by -moves, and proved that for any odd prime there exist links which are not equivalent to trivial links up to -moves by using their th Burnside groups. This gives counterexamp…
We give an algorithm for computing the Teichmüller polynomial for a certain class of fibered alternating links associated to trees. Furthermore, we exhibit a mutant pair of such links distinguished by the Teichmüller polynomial.
Symplectic quandles can detect causality in spacetimes, improving on existing methods.
New invariants derived from Seifert graphs help distinguish alternating links.
We introduce colorings of oriented surface-links by biquasiles using marked graph diagrams. We use these colorings to define counting invariants and Boltzmann enhancements of the biquasile counting invariants for oriented surface-links. We provide examples to show that the invariants can distinguish both closed surface…
In this paper we present a sequence of link invariants, defined from twisted Alexander polynomials, and discuss their effectiveness in distinguish knots. In particular, we recast and extend by geometric means a recent result of Silver and Williams on the nontriviality of twisted Alexander polynomials for nontrivial kno…
Quandle coloring detects causality in spacetime links.
The ``Links-Gould invariant'' is a two-variable Laurent polynomial invariant of oriented (1,1) tangles, which is derived from the representation of the braid generator associated with the one-parameter family of four dimensional representations with highest weights (0,0|a) of the quantum superalgebra U_q[gl(2|1)]. We u…
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…
We introduce multi-tribrackets, algebraic structures for region coloring of diagrams of knots and links with different operations at different kinds of crossings. In particular we consider the case of component multi-tribrackets which have different tribracket operations at single-component crossings and multi-componen…
New invariants distinguish spatial graphs not previously possible.
Anstee, Przyticki and Rolfsen introduced the idea of rotants, pairs of links related by a generalised form of link mutation. We exhibit infinitely many pairs of rotants which can be distinguished by Khovanov homology, but not by the Jones polynomial.
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 introduces equations to distinguish knots without using knot invariants.
We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large…
We introduce stable equivalence classes of oriented links in orientable three-manifolds that are orientation -bundles over closed but not necessarily orientable surfaces. We call these twisted links, and show that they subsume the virtual knots introduced by L. Kauffman, and the projective links introduced by Yu. Dr…
Study uses Newton polytopes to distinguish Lagrangian fillings of Legendrian submanifolds.
We consider Milnor invariants for certain covering links as a generalization of covering linkage invariants formulated by R. Hartley and K. Murasugi. A set of Milnor invariants for covering links is a cobordism invariant of a link, and that this invariant can distinguish some links for which the ordinary Milnor invaria…
The aim of this paper is to define certain algebraic structures coming from generalized Reidemeister moves of singular knot theory. We give examples, show that the set of colorings by these algebraic structures is an invariant of singular links. As an application we distinguish several singular knots and links.
A new classification theorem for links by the authors and Roger Fenn leads to computable link invariants. As an illustration we distinguish the left and right trefoils and recover the result of Carter et al that the 2-twist-spun trefoil is not isotopic to its orientation reverse. We sketch the proof the classification …
Paper generalizes pretzel links using spatial graphs.
We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We p…
Kauffman's bracket is an invariant of regular isotopy of knots and links which since its discovery in 1985 it has been used in many different directions: (a) it implies an easy proof of the invariance of (in fact, it is equivalent to) the Jones polynomial; (b) it is the basic ingredient in a completely combinatorial co…
Innovates a three-component link homotopy invariant.
New invariant distinguishes all knots up to 10 crossings.
The abstract discusses parallels between Galois theory and Stone-Weierstrass theorem in various fields.
We introduce virtual tribrackets, an algebraic structure for coloring regions in the planar complement of an oriented virtual knot or link diagram. We use these structures to define counting invariants of virtual knots and links and provide examples of the computation of the invariant; in particular we show that the in…
In this paper, we formulate a construction of ideal coset invariants for surface-links in -space using invariants for knots and links in -space. We apply the construction to the Kauffman bracket polynomial invariant and obtain an invariant for surface-links called the Kauffman bracket ideal coset invariant of sur…
We prove that if n\ge1, then an (n+1)-component Brunnian link L in a connected, oriented 3-manifold is C_n-equivalent to an unlink. We also prove that if n\ge2, then L can not be distinguished from an unlink by any Goussarov-Vassiliev finite type invariant of degree<2n.
In recent joint works of the present author with M.Prasolov and V.Shastin a new technique for distinguishing Legendrian knots has been developed. In this paper the technique is extended further to provide a tool for distinguishing transverse knots. It is shown that the equivalence problem for transverse knots with triv…
In this paper we define and give examples of a family of polynomial invariants of virtual knots and links. They arise by considering certain 22 matrices with entries in a possibly non-commutative ring, for example the quaternions. These polynomials are sufficiently powerful to distinguish the Kishino knot from …
Implemented Habegger-Lin algorithm for 4- and 5-component links.
Dihedral linking invariant uses knot colorings to distinguish knots.