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.
Innovates a three-component link homotopy invariant.
New concept of quasi-ribbon surface-links simplifies complex surface-links.
This note proves properties of surface-links with trivial components.
The paper calculates actions of string link operations for 4- and 5-component links.
The paper extends CF-moves to classify virtual links of any number of components.
Extends Benard-Conway invariant to all two-component links.
Paper finds linking numbers for Montesinos links using a simple algorithm.
In this paper, we analyze L-space surgeries on two component L-space links. We show that if one surgery coefficient is negative for the L-space surgery, then the corresponding link component is an unknot. If the link admits very negative (i.e. ) L-space surgeries, it is the Hopf link. We also give a w…
In links with two components there are three different types of crossings: self-crossings in the first component, self crossings in the second component, and crossings between components. In this paper we examine the minimum number of crossing changes needed to unlink without changing the crossings between components. …
For any link of two components in an integral homology sphere, we define an instanton Floer homology whose Euler characteristic is the linking number between the components of the link. We relate this Floer homology to the Kronheimer-Mrowka instanton Floer homology of knots. We also show that, for two-component links i…
New examples show limits of physical link isotopies.
The paper classifies links up to link-homotopy using claspers.
Two links are link-homotopic if they are transformed into each other by a sequence of self-crossing changes and ambient isotopies. The link-homotopy classes of 4-component links were classified by Levine with enormous algebraic computations. We modify the results by using Habiro's clasper theory. The new classification…
A C_n-move is a local move on links defined by Habiro and Goussarov, which can be regarded as a `higher order crossing change'. We use Milnor invariants with repeating indices to provide several classification results for links up to C_n-moves, under certain restrictions. Namely, we give a classification up to C_4-move…
We compute different versions of link Floer homology and for any -space link with two components. The main approach is to compute the -function of the filtered chain complex which is determined by the Alexander polynomials of every sublink of the -space link. As an application, Thurst…
We give infinitely many -component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any -component link with trivial Alexander polynomial. Our examples are pairwise non-concordant.
New method calculates number of components in twisted torus links.
It was shown by Jim Davis that a 2-component link with Alexander polynomial one is topologically concordant to the Hopf link. In this paper, we show that there is a 2-component link with Alexander polynomial one that has unknotted components and is not smoothly concordant to the Hopf link, answering a question of Jim D…
We construct links of arbitrarily many components each component of which is slice and yet are not concordant to any link with even one unknotted component. The only tool we use comes from the Alexander modules.
We define the crosscap number of a 2-component link as the minimum of the first Betti numbers of connected, non-orientable surfaces bounding the link. We discuss some properties of the crosscap numbers of 2-component links.
Characterizes sequences from two-component link diagrams.
We construct a graph G such that any embedding of G into R^{3} contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H contains a nonsplit n component link, where at least m of the components are nont…
We study intrinsically linked graphs where we require that every embedding of the graph contains not just a non-split link, but a link that satisfies some additional property. Examples of properties we address in this paper are: a two component link with lk(A,L) = k2^r, k not 0, a non-split n-component link where all l…
As a generalization of the linking number, we construct a set of invariant numbers for two-component handlebody-links. These numbers are elementary divisors associated with the natural homomorphism from the first homology group of a component to that of the complement of another component.
Researchers compute link surgery modules for 2-component L-space links.
For any n\ge 2, we give infinitely many unsplittable links of n components in the 3-sphere which admit non-trivial surgery yielding the 3-sphere again and whose components are mutually distinct hyperbolic knots. Berge and Kawauchi gave 2-component hyperbolic links with those two properties. We can also give infinitely …
Defines new link-homotopy invariants using Milnor's higher order link invariants.
A C_k-move is a local move that involves (k+1) strands of a link. A C_k-move is called a C_k^d-move if these (k+1) strands belong to mutually distinct components of a link. Since a C_k^d-move preserves all k-component sublinks of a link, we consider the converse implication: are two links with common k-component sublin…
We give an example of a 3-component smoothly slice boundary link, each of whose components has a genus one Seifert surface, such that any metaboliser of the boundary link Seifert form is represented by 3 curves on the Seifert surfaces that form a link with nonvanishing Milnor triple linking number. We also give a gener…
New invariants lift Milnor invariants for 3-component links.
In this paper, we study contact surgeries along Legendrian links in the standard contact 3-sphere. On one hand, we use algebraic methods to prove the vanishing of the contact Ozsváth-Szabó invariant for contact -surgery along certain Legendrian two-component links. The main tool is a link surgery formula for Heeg…
We give new examples of 2-component links with linking number one and unknotted components that are topologically concordant to the positive Hopf link, but not smoothly so - in fact they are not smoothly concordant to the positive Hopf link with a knot tied in the first component. Such examples were previously construc…
Four-dimensional surgery is used to show that a two component link with Alexander polynomial one is topologically concordant to the Hopf link.
We show that there are links whose individual components are concordant to the unknot, but which are not concordant to any link with unknotted components. We give examples in the topological category, and examples in the smooth category which are topologically slice. We also give generalizations regarding components of…
We give a classification of -component links up to -move. In order to prove this classification, we characterize Brunnian links, and have that a Brunnian link is ambient isotopic to a band sum of trivial link and Milnor's links.
No characterizing slopes for multi-component links.
This paper provides a relationship between a geometric structure of a suspended tree and the number of link components of the associated link diagram.
We provide necessary conditions for the Alexander polynomials of algebraically split component-preservingly amphicheiral links. We raise a conjecture that the Alexander polynomial of an algebraically split component-preservingly amphicheiral link with even components is zero. Our necessary conditions and some examples …
The paper studies hyperbolic geometry of links formed by adding trivial components to knots.
New methods for delta-moves on algebraically split links identified.
Researchers debunk a generalized Property R conjecture for 2-component links.
The study finds counterexamples to a conjecture about incompressible planar surfaces in hyperbolic link exteriors.
Study extends knot genus results to two-component alternating links.
The paper generalizes linking number properties for complete graphs.
New spheres can split a 4D link in ways not possible in 3D.
Aicardi's invariant is extended to colored singular links using graphical calculus.
Study shows how Khovanov homology behaves for split links and cobordisms.
We study Heegaard Floer homology and various related invariants (such as the -function) for two-component L-space links with linking number zero. For such links, we explicitly describe the relationship between the -function, the Sato-Levine invariant and the Casson invariant. We give a formula for the Heegaard Fl…