Related papers: Concordance to links with an unknotted component
The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…
We show that there are only finitely many homogeneous links whose Conway polynomial has any given degree. Using this we give an example of an inhomogeneous, fibred knot. Secondly, we show how to compute the monodromy of a homogeneous link…
Modular structure is pervasive in many complex networks of interactions observed in natural, social and technological sciences. Its study sheds light on the relation between the structure and function of complex systems. Generally speaking,…
We construct an algorithm to decide whether two given Legendrian or transverse links are equivalent. In general, the complexity of the algorithm is too high for practical implementation. However, in many cases, when the symmetry group of…
Tying knots and linking microscopic loops of polymers, macromolecules, or defect lines in complex materials is a challenging task for material scientists. We demonstrate the knotting of microscopic topological defect lines in chiral nematic…
We study the structure of the augmented fundamental quandle of a knot whose complement contains an incompressible torus. We obtain the relationship between the fundamental quandle of a satellite knot and the fundamental quandles/groups of…
We describe a construction procedure of infinite sets of $2$-links in closed simply connected 4-manifolds that are topologically isotopic, smoothly inequivalent and componentwise topologically unknotted. These 2-links are the first examples…
We show that there exists a link with 2 components which is not smoothly slice in $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$. By contrast, it is well-known that every knot (i.e., link with 1 component) is smoothly slice therein. Our proof…
The knot Floer complex and the concordance invariant $\varepsilon$ can be used to define a filtration on the smooth concordance group. We exhibit an ordered subset of this filtration that is isomorphic to $\mathbb{N} \times \mathbb{N}$ and…
Links and knots are exotic topological structures that have garnered significant interest across multiple branches of natural sciences. Coherent links and knots, such as those constructed by phase or polarization singularities of coherent…
Independent Component Analysis (ICA) offers interpretable semantic components of embeddings. While ICA theory assumes that embeddings can be linearly decomposed into independent components, real-world data often do not satisfy this…
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…
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,…
The forbidden moves in virtual knot theory can be used to unknot any knot, virtual or classical; however, multi-component crossings in links can still survive, resulting a fused link. Using the forbidden moves, we categorify fused links…
We call a knot $K$ a complete Alexander neighbor if every possible Alexander polynomial is realized by a knot one crossing change away from $K$. It is unknown whether there exists a complete Alexander neighbor with nontrivial Alexander…
Jones introduced a method to produce unoriented links from elements of the Thompson's group $F$, and proved that any link can be produced by this construction. In this paper, we attempt to investigate the relations between conjugacy classes…
We show that if a split link is obtained from a split link $L$ in $S^3$ by $1/n$-Dehn surgery along a trivial knot $C$, then the link $L\cup C$ is splittable. That is to say, it is impossible to obtain a split link from a split link via a…
We use techniques of Freedman and Teichner to prove that, under certain circumstances, the multi-infection of a slice link is again slice (not necessarily smoothly slice). We provide a general context for proving links are slice that…
Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers.…
As a corollary of work of Ozsvath and Szabo [math.GT/0301149], it is shown that the classical concordance group of algebraically slice knots has an infinite cyclic summand and in particular is not a divisible group.