Related papers: Alexander Quandles and Detecting Causality

We prove that the detection rate of n-crossing alternating links by many standard link invariants decays exponentially in n, implying that they detect alternating links with probability zero. This phenomenon applies broadly, in particular…

Recently, it has been shown that the Jones polynomial, in [LS19], and the Alexander polynomial, in [NT18], of rational knots can be obtained by specializing $F$-polynomials of cluster variables. At the core of both results are continued…

In this paper we conjecture that the Links-Gould invariant of links, that we know is a generalization of the Alexander-Conway polynomial, shares some of its classical features. In particular it seems to give a lower bound for the genus of…

This paper verifies a conjecture of Edelman and Reiner regarding the homology of the $h$-complex of a Boolean algebra. A discrete Morse function with no low-dimensional critical cells is constructed, implying a lower bound on connectivity.…

We construct the universal sl(2)-tangle cohomology using an approach with webs and dotted foams. This theory depends on two parameters, and for the case of links it is a categorification of the unnormalized Jones polynomial of the link.

Earlier it was described to which extent the Alexander polynomial in several variables of an algebraic link in the Poincar\'e sphere determines the topology of the link. It was shown that, except some explicitly described cases, the…

We prove that the length of any gap in the differential grading of the Khovanov homology of any quasi-alternating link is one. As a consequence, we obtain that the length of any gap in the Jones polynomial of any such link is one. This…

Learning the unique directed acyclic graph corresponding to an unknown causal model is a challenging task. Methods based on functional causal models can identify a unique graph, but either suffer from the curse of dimensionality or impose…

The Alexander biquandle of a virtual knot or link is a module over a 2-variable Laurent polynomial ring which is an invariant of virtual knots and links. The elementary ideals of this module are then invariants of virtual isotopy which…

Background: Although Alzheimer's disease (AD) is a central nervous system disease and type 2 diabetes mellitus (T2DM) is a metabolic disorder, an increasing number of genetic epidemiological studies show clear link between AD and T2DM. The…

This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics.

We introduce a new invariant of tangles along with an algebraic framework in which to understand it. We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of…

We use the 2-loop term of the Kontsevich integral to show that there are (many) knots with trivial Alexander polynomial which don't have a Seifert surface whose genus equals the rank of the Seifert form. This is one of the first…

Hawking's stable causality implies Sorkin and Woolgar's K-causality. The work investigates the possible equivalence between the two causality requirements, an issue which was first considered by H. Seifert and then raised again by R. Low…

In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of…

Let l be a link of d components. For every finite-index lattice in Z^d there is an associated finite abelian cover of S^3 branched over l. We show that the order of the torsion subgroup of the first homology of these covers has exponential…

We show two results about the Conway potential function which is known as the normalized multivariable Alexander polynomial. We first show that the Conway potential function introduced by Kauffman in "Formal Knot Theory" is indeed a link…

We propose a constraint-based algorithm, which automatically determines causal relevance thresholds, to infer causal networks from data. We call these topological thresholds. We present two methods for determining the threshold: the first…

Joyce showed that for a classical knot $K$, the involutory medial quandle $\text{IMQ}(K)$ is isomorphic to the core quandle of the homology group $H_1(X_2)$, where $X_2$ is the cyclic double cover of $\mathbb S ^3$, branched over $K$. It…

For a 2-periodic link $\tilde L$ in the thickened annulus and its quotient link $L$, we exhibit a spectral sequence with $E^1 \cong AKh(\tilde L) \otimes_{\mathbb{F}_2} \mathbb{F}_2[\theta, \theta^{-1}] \rightrightarrows E^\infty \cong…