Related papers: Linking number and Milnor invariants
Topological polymers have various topological types, and they are expressed by graphs. However, the Jones polynomial, we have a difficulty to compute it; computational time is growing exponentially with respect to the crossing number. The…
In this note we define a polynomial invariant for colored links by a skein relation. It specializes to the Jones polynomial for classical links.
This paper is a survey on invariants of representations of quivers and their generalizations. We present the description of generating systems for invariants and relations between generators.
Both a general and a diagonal u-invariant for forms of higher degree are defined, generalizing the u-invariant of quadratic forms. Both old and new results on these invariants are collected.
This paper describes the relationship between the first non-vanishing Milnor invariants of a classical link and the intersection invariant of a twisted Whitney tower. This is a certain 2-complex in the 4-ball, built from immersed disks…
In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…
This note extends the invariant defined in "An invariant of metric spaces under bornologous equivalences" to the coarse category.
We study the quandle counting invariant for a certain family of finite quandles with trivial orbit subquandles. We show how these invariants determine the linking number of classical two-component links up to sign.
The subfactor approach to modular invariants gives insight into the fusion rule structure of the modular invariants.
In this paper, we define some polynomial invariants for virtual knots and links. In the first part we use Manturov's parity axioms to obtain a new polynomial invariant of virtual knots. This invariant can be regarded as a generalization of…
The notion of modular covariance is reviewed and the reconstruction of the Poincar\'e group extended to the low-dimensional case. The relations with the PCT symmetry and the Spin and Statistics theorem are described.
This paper generalizes the bordered-algebraic knot invariant introduced in an earlier paper, giving an invariant now with more algebraic structure. It also introduces signs to define these invariants with integral coefficients. We describe…
In this paper, we define invariants of links in terms of colorings of link diagrams and prove that these invariants coincide with various notions of widths of links with respect to the standard Morse function. Our formulations are…
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.
Coloring numbers are one of the simplest combinatorial invariants of knots and links to describe. And with Joyce's introduction of quandles, we can understand them more algebraically. But can we extend these invariants to tangles -- knots…
In the present paper we extend the definition of slice-torus invariant to links. We prove a few properties of the newly-defined slice-torus link invariants: the behaviour under crossing change, a slice genus bound, an obstruction to strong…
Fixing two concordant links in $3$--space, we study the set of all embedded concordances between them, as knotted annuli in $4$--space. When regarded up to surface-concordance or link-homotopy, the set $\mathcal{C}(L)$ of concordances from…
We define an annular concordance invariant and study its properties. When specialized to braids, this invariant gives bounds on band rank. We introduce a modified chain complex to reformulate the invariant. Then, by focusing on a special…
An efficient numerical algorithm for the computation of linking number is presented. The algorithm keep tracks or rounding error so that it can ensure the correctness of the results.
In this short paper, we explore relationship between various models of complex networks with pinning controllers.