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.
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48 results for “link classification”
Classifies Legendrian torus and cable links, revealing symmetries and invariants.
problem Classifying Legendrian torus and cable links.
method Classification through Legendrian and transversal isotopies, symmetries analysis.
result First family of non-destabilizable links without maximal Thurston-Bennequin invariant.
The paper classifies links up to link-homotopy using claspers.
problem Classifying links up to link-homotopy.
method Using Habiro's clasper calculus, defining a linear representation of the homotopy braid group, and providing a geometric proof.
result Geometric proof of Levine's classification of 4-component links and further classification of 5-component links in the algebraically split case.
We generalized the periodic links to \emph{transitive} links in a -manifold . We find a complete classification theorem of transitive links in a -dimensional sphere . We study these links from several different aspects including polynomial invariants using the relation between link polynomials of…
Complete classification of handlebody links up to six crossings.
problem Classifying handlebody links with specific properties.
method Complete enumeration and ambient isotopy consideration.
result Complete classification of handlebody links with six crossings or less.
A pass-move and a $#$-move are local moves on oriented links defined by L.H. Kauffman and H. Murakami respectively. Two links are self pass-equivalent (resp. self $#$-equivalent) if one can be deformed into the other by pass-moves (resp. $#$-moves), where non of them can occur between distinct components of the link. T…
Complete classification of links up to specific moves.
problem Classifying links using specific local moves.
method Clasper theory.
result Complete classification of links up to clasp-pass moves.
Two string links are equivalent up to -moves and link-homotopy if and only if their all Milnor link-homotopy invariants are congruent modulo . Moreover, the set of the equivalence classes forms a finite group generated by elements of order . The classification induces that if two string links are equivalent u…
CF-moves for virtual linksmath.GT
The paper extends CF-moves to classify virtual links of any number of components.
problem Classifying virtual links using CF-moves.
method Extending CF-moves to classify virtual links of arbitrary number of components using the virtual linking number and invariants.
result Classification of 3-component even virtual links up to CF-moves.
On C_n-moves for linksmath.GT
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…
The paper calculates actions of string link operations for 4- and 5-component links.
problem Classifying link-homotopy classes of string links.
method Explicit calculation of actions of partial conjugations and conjugations for 4- and 5-component string links.
result Presentations of link-homotopy classes for 4- and 5-component links.
Classifies exceptional Legendrian realizations of Hopf link connected sums.
problem Classifying exceptional Legendrian realizations of Hopf link connected sums.
method Complete coarse classification using Legendrian knot theory.
result First classification result about exceptional Legendrian representatives for Hopf link connected sums.
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the calculus of continued fractions. We characterize the class of strongly invertib…
Flat plumbing basket surfaces of links were introduced to study the geometry of the complement of the links. In present article, we study links of the flat plumbing basket numbers or less using a special presentation of the flat plumbing basket surfaces. We find a complete classification theorem of links of the fla…
Classifies links with small Khovanov homology ranks.
problem Classifying links with specific ranks in Khovanov homology.
method Previous results combined with new classifications.
result All links with ranks ≤ 8 and three-component links with ranks ≤ 12 are classified.
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 simplifies link classification in 3-sphere using braids and templates.
problem Classify links in the 3-sphere.
method Simplified braid description, generalised T-links, bunch algorithm.
result Established upper volume bound for 3-manifolds.
In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of J.S. Birman and H.M. Hilden on the relation between bridge presentations of links and Heegaard splittings of 3-manifolds. In the …
N-quandles of linksmath.GT
Classifies links with finite N-quandles for some N.
problem Describing finite quotients of quandles, especially -quandles.
method Introducing and studying -quandles, proving one direction of a conjectured classification.
result Proves one direction of a conjectured classification of links with finite -quandles.
Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper we consider ribbon tubes and ribbon torus-link…
Link prediction in a graph is the problem of detecting the missing links that would be formed in the near future. Using a graph representation of the data, we can convert the problem of classification to the problem of link prediction which aims at finding the missing links between the unlabeled data (unlabeled nodes) …
Graph-based multi-label classifier extends CULP for multi-label data.
problem Solving multi-label classification problems.
method Extends CULP algorithm to handle multi-label data.
result Competitive results compared to cutting-edge multi-label classifiers.
Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our mai…
The paper classifies virtual links using the arc shift operation.
problem Classifying \( n \)-component virtual links up to arc shift equivalence.
method Established the arc shift operation as an unknotting tool for \( n \)-homogeneous proper virtual links, explored its connection to the odd writhe, and identified sequences with specific arc shift bounds.
result Identified sequences of virtual link diagrams \( L_n \) with an upper bound of arc shift number equal to \( n \).
Classifies Legendrian Hopf links in lens spaces.
problem Classifying Legendrian Hopf links in lens spaces.
method Complete classification using contact surgery diagrams.
result Explicit algorithm for all Legendrian representatives.
The paper classifies pretzel links with 2 components and gives conditions for those with 3 or more.
problem Classifying pretzel links based on their self delta-equivalence.
method Using Conway polynomials to determine self delta-equivalence for links with 2 or more components.
result Necessary and sufficient conditions for self delta-equivalence of pretzel links with 3 or more components.
In this note, we complete the classification of quasi-alternating Montesinos links. We show that the quasi-alternating Montesinos links are precisely those identified independently by Qazaqzeh-Chbili-Qublan and Champanerkar-Ording. A consequence of our proof is that a Montesinos link is quasi-alternating if and onl…
We prove that a sufficiently large surgery on any algebraic link is an L-space. For torus links we give a complete classification of integer surgery coefficients providing L-spaces.
We give a concise proof of a classification of lens spaces up to orientation-preserving homeomorphisms. The chief ingredient in our proof is a study of the Alexander polynomial of ` symmetric' links in .
Collective classification has been intensively studied due to its impact in many important applications, such as web mining, bioinformatics and citation analysis. Collective classification approaches exploit the dependencies of a group of linked objects whose class labels are correlated and need to be predicted simulta…
In this paper, we introduce a neural network framework for semi-supervised clustering (SSC) with pairwise (must-link or cannot-link) constraints. In contrast to existing approaches, we decompose SSC into two simpler classification tasks/stages: the first stage uses a pair of Siamese neural networks to label the unlabel…
Characterizes arithmetic and commensurable links in curved surfaces.
problem Classifying arithmetic and commensurable links in curved surfaces.
method Combines symmetry arguments, combinatorial geometry, and number-theoretic data.
result Characterizes arithmetic and commensurable right-angled tiling links.
In this paper we define and study flexible links and flexible isotopy in projective space. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholms interpretation of Viros encomplexed writhe.
This work classifies belted sum decompositions of fully augmented links.
problem Understanding belted sum decompositions of fully augmented links.
method Explicit classifications of thrice punctured spheres in FAL complements, geometric, combinatorial, and diagrammatic characterizations.
result Every FAL complement canonically decomposes into FALs which are either prime or two-fold covers of the Whitehead link.
Classifies small links in an unmarked solid torus.
problem Classifying knots and links in an unmarked solid torus.
method Invariants and Dehn twists to detect and transform links.
result Classification of all non-split links up to 6 crossings.
The paper classifies links with low rank knot Floer and Khovanov homologies.
problem Detecting and classifying links with low rank knot Floer and Khovanov homologies.
method Generalized link Floer homology, used to obtain rank bounds and classify links.
result Knot Floer homology detects and .
New upper bound on Jones polynomial for fibered positive links.
problem Classifying positive and non-positive knots of crossing number ≤ 12.
method Proved a new upper bound on the maximum degree of Jones polynomial for fibered positive knots.
result Maximum degree of Jones polynomial for fibered positive knots is at most four times the minimum degree.
The paper classifies links based on signature and crossing number properties.
problem Understanding the relationship between signature and crossing number of knots and links.
method Refined theorems and comprehensive classification of links with specific properties.
result Identification of all links where signature + crossing number = 2, closures of positive 3-braids.
Paper proves unique canonical form for certain highly twisted knots and links.
problem Classifying knots and links with specific plat projections.
method Analyzes -plat projections with specific constraints on crossings and heights.
result Unique canonical form for certain knots and links with plat projections.
Proposes a method to enhance graph models by injecting unseen connections.
problem Enhancing graph models to utilize unseen connections.
method Parametric link injection layer to find and inject weak connections.
result Improves performance on node classification and link prediction tasks.
A link of an isolated singularity of a two-dimensional semialgebraic surface in is a knot (or a link) in . Thus the ambient Lipschitz classification of surface singularities in can be interpreted as a bi-Lipschitz refinement of the topological classification of knots (or links) in . We show that, …
Given a clover link, we construct a bottom tangle by using a disk/band surface of the clover link. Since the Milnor number is already defined for a bottom tangle, we define the Milnor number for the clover link to be the Milnor number for the bottom tangle and show that for a clover link, if Milnor numbers of length k …
Paper classifies link diagrams on nonorientable surfaces using region crossing changes.
problem Classifying link diagrams on nonorientable surfaces.
method Classification through region crossing changes.
result Classification of link diagrams on nonorientable surfaces.
Let P be a closed smooth (4j-2)-connected 8j-manifold. We complete Wilkens' classification of the manifolds P for j = 1,2 and give an alternative proof to Wall's classification of the manifolds for j > 2. The Hopf-invariant-one dimensions (j=1,2) are characteristed by the fact that the quadratic linking functions which…
-quandles of spatial graphsmath.GT
Classifies spatial graphs with finite N-quandles.
problem Determining isomorphism of spatial graphs' N-quandles.
method Generalized N-quandles to spatial graphs, proving basic results and conjecturing a classification.
result Verifies conjecture in several cases, presents a possible counterexample.
The paper classifies twisted torus links that are unlinks.
problem Identifying conditions for twisted torus links to be unlinks.
method Characterization of parameter families for unlinking twisted torus links.
result Complete characterization of parameter families for unlinking twisted torus links.
This paper gives two new combinatorial topological proofs of the classification of rational tangles. Each proof rests on an elegant lemma showing that rational tangles are isotopic to canonical alternating rational tangles. The first proof defines the tangle fraction from the canonical form and uses flyping to prove in…
Cobordism of virtual string links on strands is a combinatorial generalization of link cobordism. There exists a bijection between virtual string links up to cobordisms and elements of the group . This paper also shows that virtual string links up to unwelded equivalence are classified by those…