New representation connects two link invariants.
problem Link invariants of different types.
method Augmentation representation of link group.
result Connects two types of link invariants.
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48 results for “link representation”
The Tong-Yang-Ma representations are extended to string links and welded string links.
problem Extending Tong-Yang-Ma representations to string links and welded string links.
method Using the method of Silver and Williams, the authors extend the Tong-Yang-Ma representations.
result The kernels of the extended representations can be described using linking numbers.
New invariant counts SU(2) representations for links.
problem Counting irreducible SU(2) representations for links.
method Signed count of irreducible representations with fixed traces.
result Invariant is a sum of multivariable signatures for specific links.
Link groups can only have certain SU(2) representations.
problem Characterizing SU(2) representations of link groups.
method Analyzing the structure of link groups and their representations in SU(2).
result Irreducible SU(2) representations of link groups are restricted to specific configurations.
Satellite links with many twists have simpler companions.
problem Relationship between satellite and companion links' complexity.
method Constructing satellite links with multiple full twists and analyzing their companion links.
result Satellite links with many twists have simpler companion links.
Study representation varieties of twisted Hopf links using combinatorial and Hodge theory.
problem Representation theory of Hopf link complements with n twists.
method Combinatorial problem and equivariant Hodge theory.
result Close formulas for E-polynomials of representation and character varieties for ranks 2 and 3.
A realization of a virtual link diagram is obtained by choosing over/under markings for each virtual crossing. Any realization can also be obtained from some representation of the virtual link. (A representation of a virtual link is a link diagram on an oriented 2-dimensional surface.) We prove that if a minimal genus …
Study Legendrian links using representations and sheaves.
problem Understanding Legendrian links through algebraic and geometric representations.
method Investigate an category of -dimensional representations and conjecture equivalence to sheaves.
result Established cohomological equivalence for Legendrian torus links.
The paper introduces two-tone colorings for links and shows conditions for surjective dihedral representations.
problem The challenge is to find conditions for links to admit surjective dihedral representations.
method The method involves introducing two-tone colorings and providing conditions for the link groups to admit such representations.
result Any link with at least 3 components admits a surjective homomorphism to the dihedral group of arbitrary degree.
Explains how knots and links can be shown using braids.
problem None explicitly stated; focuses on representation methods.
method Diagrammatic representations of knots and links via braids.
result Explains how braids can represent knots and links.
New method for calculating colored HOMFLY-PT polynomials for links with different symmetric representations.
problem Calculating colored HOMFLY-PT polynomials for links with arbitrary symmetric representations.
method Using quantum Racah coefficients (6j-symbols) of to simplify the evaluation.
result Multi-colored link polynomials for a specific link L7a3 are successfully evaluated.
State sums for quantum link invariants from a specific representation.
problem Calculating quantum link invariants from a specific representation of U_q(gl_{N|M}).
method Using state sums and representation theory of U_q(gl_{N|M}).
result Explicit relation with Kashaev invariants for the N-th exterior power of the standard representation.
The paper connects Apollonian packings to knot theory and improves link representations.
problem Realizing algebraic links in Apollonian packings.
method Introducing new representations of links in tangency graphs of sphere packings, proving link realizability, and improving upper bounds.
result Any algebraic link can be realized in the cubic section of the orthoplicial Apollonian packing.
Multiplicity of non-acyclic -representations and L-functions of the odd-twisted Whitehead linksmath.GT
Study multiplicity of non-acyclic SL2-representations and L-functions of Whitehead links.
problem Understanding the multiplicity of non-acyclic SL2-representations and their L-functions.
method Geometric interpretation of Reidemeister torsion divisors and application to L-functions.
result Prove multiplicity two for odd-twisted Whitehead links.
Given a link , a representation is {\it tracefree} if the image of each meridian has trace zero. We determine the conjugacy classes of tracefree representations when is a Montesinos link.
Given a link , a representation is {\it trace-free} if it sends each meridian to an element with trace zero. We present a method for completely determining trace-free -representations for arborescent links. Concrete computations are done for a …
Stratifies representation varieties of twisted Hopf links.
problem Stratifying representation varieties of twisted Hopf links.
method Using stratification of -representation varieties of the fundamental group of the complement of a twisted Hopf link.
result Explicit description and computation of motives for ranks 1 and 2.
New Khovanov homology for marked links collapses spectral sequence.
problem Understanding instanton theory and its relation to Khovanov homology.
method Introducing marked Khovanov homology and studying its properties.
result Khovanov homology for alternating links does not depend on marking data for non-split links.
Autoencoder learns graph representations for link prediction and node classification.
problem Link prediction and semi-supervised node classification on graphs.
method A novel autoencoder architecture for joint local graph structure and node feature learning.
result Significant improvement over related methods for graph representation learning.
New invariants for virtual knots and links defined via quiver representations.
problem Defining new invariants for virtual knots and links.
method Quiver representations associated to virtual biquandles and rings.
result New polynomial invariants for virtual knots and links.
The paper defines new representations and groups related to virtual links.
problem Defining and studying new representations of virtual braid groups and link groups.
method Introducing virtually symmetric representations, virtual link groups, and marked Gauss diagrams.
result Established equivalence of many known representations to virtually symmetric representations.
In this paper we investigate the virtual string links via a probabilistic interpretation. This representation can be used to distinguish some virtual string links from classical string links. In order to study the algebraic structure behind this probabilistic interpretation we introduce the notion of virtual flat biqua…
Efficient method for computing twisted Alexander polynomials of Montesinos links.
problem Computing twisted Alexander polynomials for Montesinos links efficiently.
method Developed an efficient method to compute the twisted Alexander polynomial for Montesinos links using any linear representation.
result Formulas for multi-variable Alexander polynomials can be easily derived.
Extends Benard-Conway invariant to all two-component links.
problem Counting irreducible SU(2) representations for two-component links.
method Counting irreducible SU(2) representations with fixed meridional traces.
result Invariant equals symmetrized multivariable link signature for (2, 2n)-torus links.
This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be seen as exterior powers of …
A new autoencoder learns graph representations for link prediction and node classification.
problem Link prediction and node classification on graph data.
method Multi-task graph autoencoder architecture.
result Significant improvement over three baselines on five graph datasets.
The paper studies parabolic representations of 2-bridge links using symplectic quandles.
problem Parabolic representations of 2-bridge links.
method Convert conjugation quandle equations to symplectic quandle equations, using a polynomial to find arc coloring vectors.
result Explicit formulas for parabolic representations of 2-bridge links are derived, including complex volume and cusp shape.
We describe a family of representations in SL(3,) of the fundamental group of the Whitehead link complement. These representations are obtained by considering pairs of regular order three elements in SL(3,) and can be seen as factorising through a quotient of defined by a certain exception…
Study links using Soergel bimodules and Serre duality.
problem Computing the triply-graded homology of the Whitehead link.
method Representability of partial trace functors and diagrammatics for Hochschild cohomology.
result Computed the triply-graded homology of the Whitehead link.
Using the recently proposed differential hierarchy (Z-expansion) technique, we obtain a general expression for the HOMFLY polynomials in two arbitrary symmetric representations of link families, including Whitehead and Borromean links. Among other things, this allows us to check and confirm the recent conjecture of arX…
We present a new link invariant which depends on a representation of the link group in SO(3). The computer calculations indicate that an abelian version of this invariant is expressed in terms of the Alexander polynomial of the link. On the other hand, if we use non abelian representation, we get the squared non abelia…
The paper enhances representations to show left-orderability of certain 3-manifold groups.
problem Left-orderability of 3-manifold groups using enhanced representations.
method Recalibration of Calegari and Dunfield's flipping construction for $\mbox{Homeo}_+(S^1)$-representations.
result Branched covers of links are left-orderable, generalizing known results.
A book representation of a graph is a particular way of embedding a graph in three dimensional space so that the vertices lie on a circle and the edges are chords on disjoint topological disks. We describe a set of operations on book representations that preserves ambient isotopy, and apply these operations to , t…
New unitary representations for Thompson's group V and virtual links.
problem Constructing unitary representations for Thompson's group V and virtual links.
method Defining a surjection from V to virtual equivalence classes of CC links, constructing unitary representations from kei and operator quandle colorings.
result Realizes all oriented almost classical virtual links.
New 2-representations link spectral enhancements in link homology.
problem Spectral enhancements in link homology.
method Skew Howe duality, frames, and multifunctors.
result Spectral 2-representations of categorified quantum groups.
There are some similarities between cohomology of SU(2)-representation varieties of the fundamental group of some link complements and the Khovanov homology of the links. We start here a program to explain a possible source of these similarities. We introduce a symplectic manifold with an action of the b…
Invariants for 3-manifolds with embedded links using Hopf algebras.
problem Constructing invariants for 3-manifolds with embedded framed links.
method Using involutory Hopf algebras and representations of Drinfeld double.
result The invariant recovers known invariants for specific cases.
Link between braid groups and q-deformed rationals solves a classification problem.
problem Classifying faithful complex specializations of the Burau representation of braid group B3.
method Established a link between Burau representation and q-deformed rational numbers.
result Proved faithfulness of Burau representation outside a specific annulus.
Curved Rickard complexes extend link homologies to arbitrary representations.
problem Link homologies for arbitrary representations.
method Definition and study of curved Rickard complexes.
result Deformations of link homologies generalize previous work.
New method associates annular links to elements of Thompson's group T.
problem Associating annular links to elements of Thompson's group T.
method Edge-signed graphs embedded in annuli and unitary representations of T.
result Tait graphs of annular links can be constructed from elements of T.
The paper explores symmetric representations of links and conditions for amphichirality.
problem Investigating symmetric representations of links and conditions for amphichirality.
method Using antipodally self-dual and antipodally symmetric maps, the authors provide sufficient combinatorial conditions for amphichirality.
result A link is amphichiral if its self-dual pairing is not one of 6 specific ones.
Researchers describe character varieties for Hopf links, proving geometric properties.
problem Character variety geometry of Hopf links with twists.
method Geometric descriptions of irreducible and totally reducible representations.
result Complete geometric description of -character variety for .
Braids for pretzel linksmath.GT
A method to convert pretzel links into braids.
problem Representing pretzel links as braids.
method General procedure to convert any pretzel link into a braid.
result A specific braid word corresponding to the pretzel link.
New method calculates Alexander polynomial from mixed braid representations.
problem Calculating Alexander polynomials for links in lens spaces.
method Reduced Burau-like representation for mixed braid group, direct calculation from mixed braid.
result Direct calculation of Alexander polynomial from mixed braid representations.
In a "naive" attempt to create algebraic quantum field theories on the circle, we obtain a family of unitary representations of Thompson's groups T and F for any subfactor. The Thompson group elements are the "local scale transformations" of the theory. In a simple case the coefficients of the representations are polyn…
The paper develops a new theory for quantum link invariants using quandles and biquandles.
problem Quantum link invariants for links with flat connections.
method Using quandles and biquandles, the paper extends Reshetikhin-Turaev functor to tangles.
result A new invariant of links with a gauge class of quandle representations.
In this paper we study the relation between two diagrammatic representations of links in lens spaces: the disk diagram and the grid diagram and we find how to pass from one to the other. We also investigate whether the HOMFLY-PT invariant and the Link Floer Homology are essential invariants, that is, we try to understa…
Relational data representations have become an increasingly important topic due to the recent proliferation of network datasets (e.g., social, biological, information networks) and a corresponding increase in the application of statistical relational learning (SRL) algorithms to these domains. In this article, we exami…