The study finds hyperbolic twisted torus links for certain twists.
problem Identifying hyperbolic twisted torus links.
method Analyzing -torus links with strands twisted times.
result All hyperbolic twisted torus links are identified for .
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48 results for “twisted link”
The paper introduces colorings and invariants for twisted links and shows how double coverings can be equivalent.
problem Understanding and distinguishing twisted links.
method Twisted intersection colorings and double coverings.
result There exist infinitely many pairs of twisted links with equivalent double coverings.
Paper discusses when virtual links are equivalent as twisted links.
problem Determining equivalence of virtual links as twisted links.
method Using stable equivalence classes of links in oriented thickenings of surfaces.
result Necessary and sufficient condition for virtual links to be equivalent as twisted links.
New algebraic structure for distinguishing twisted virtual handlebody-links.
problem Distinguishing twisted virtual handlebody-links.
method Introducing twisted virtual bikeigebras and using them to define invariants.
result New invariants distinguish some twisted virtual handlebody-links.
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.
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.
The paper classifies hyperbolic and satellite T-links formed by twisting.
problem Classifying hyperbolic and satellite T-links formed by twisting.
method Classification through Dehn filling and analysis of parent links.
result Classification of hyperbolic and satellite T-links formed by twisting.
A virtual link can be understood as a link in a trivial I-bundle over an orientable compact surface with genus. A twisted virtual link is a link in a trivial I-bundle over a not-necessarily orientable compact surface. A twisted virtual birack is an algebraic structure with axioms derived from the twisted virtual Reidem…
Computed A-polynomial of twisted Whitehead links.
problem Calculating the A-polynomial for a specific class of links.
method Direct computation of the A-polynomial using mathematical techniques.
result Determined canonical components and volume formula for twisted Whitehead links.
The paper confirms a conjecture and extends arrow polynomial to twisted links.
problem Extending classical invariants to virtual and twisted links.
method Checkerboard framings, cut points, and normalized arrow polynomial.
result The normalized arrow polynomial is an invariant for twisted links.
The twisting technique creates infinite links.
problem Creating infinite links from given ones.
method Applying the twisting technique to adequate, homogeneous, or alternative links.
result These three classes of links are infinite.
New method calculates number of components in twisted torus links.
problem Determining the number of components of twisted torus links.
method Euclidean algorithm-like procedure based on parameters.
result Number of components is a multiple of gcd(p, q, r, s).
Twisted links are a generalization of virtual links. As virtual links correspond to abstract links on orientable surfaces, twisted links correspond to abstract links on (possibly non-orientable) surfaces. In this paper, we introduce the notion of the double covering of a twisted link. It is defined by considering the o…
The paper extends knot theory to twisted virtual braids and links.
problem Generalizing knot theory to include twists.
method Introduced twisted virtual braids and proved theorems for twisted links.
result The Alexander and Markov theorems were extended to twisted links.
New bounds on categorified link invariants using fractional Dehn twist coefficients.
problem Bounding ranks of categorified link invariants.
method Using fractional Dehn twist coefficients and link Floer homology.
result Lower bounds on ranks of categorified link invariants.
Twisted links are obtained from a base link by starting with a -braid representation, choosing several () adjacent strands, and applying one or more twists to the set. Various restrictions may be applied, e.g. the twists may be required to be positive or full twists, or the base braid may be required to have a ce…
Study on singular twisted links and virtual braids, extending knot theory concepts.
problem Extending knot theory concepts to singular twisted links and virtual braids.
method Definition and analysis of singular twisted virtual braids and their monoid structure.
result Presentation of monoid and reduced monoid for singular twisted virtual braids.
It follows from earlier work of Silver-Williams and the authors that twisted Alexander polynomials detect the unknot and the Hopf link. We now show that twisted Alexander polynomials also detect the trefoil and the figure-8 knot, that twisted Alexander polynomials detect whether a link is split and that twisted Alexand…
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.
Study classifies exceptional surgeries on specific links.
problem Classifying exceptional Dehn surgeries on specific links.
method Examined minimally twisted seven-chain links.
result Classified all exceptional Dehn surgeries on the links.
Twisted torus knots and links are given by twisting adjacent strands of a torus link. They are geometrically simple and contain many examples of the smallest volume hyperbolic knots. Many are also Lorenz links. We study the geometry of twisted torus links and related generalizations. We determine upper bounds on their …
Stability of Jones polynomial coefficients under twist regions.
problem Stability of colored Jones polynomial coefficients.
method Proof of coefficient stabilization under twist regions.
result Stabilization of coefficients in alternating links.
We show that for a large class of hyperbolic knots and links, we can determine bounds on the volume of the link complement from combinatorial information given by a link diagram. Specifically, there is a universal constant C such that if a knot or link admits a prime, twist reduced diagram with at least 2 twist regions…
Paper discusses a new link invariant from virtual link theory.
problem Developing a new invariant for twisted links.
method Using JKSS invariant of virtual links and double coverings.
result Derived a new invariant for twisted links.
New measure shows how links can be untangled as twists increase.
problem Understanding how links can be simplified through repeated twists.
method Introduced the stable unknotting number to analyze links in a twist family.
result The stable unknotting number depends only on the winding number of the link, not the wrapping number.
Improved bounds on volume-det inequality for links with many twists.
problem Vol-Det Conjecture for highly twisted alternating links.
method Improved Burton's and Stoimenow's bounds for links with more than eight twists.
result Enhanced inequalities for volume and determinant of links with many twists.
A new twist on Lorenz linksmath.GT
Twisted torus links are given by twisting a subset of strands on a closed braid representative of a torus link. T--links are a natural generalization, given by repeated positive twisting. We establish a one-to-one correspondence between positive braid representatives of Lorenz links and T--links, so Lorenz links and T-…
Invariants for virtual and twisted links using affine indices.
problem Computing invariants for virtual and twisted links.
method Using affine indices to define invariants for virtual and twisted links.
result Invariants for virtual and twisted links computed using affine indices.
Study Alexander matrices for link quandles and their relation to knot invariants.
problem Understanding Alexander matrices for link quandles and their applications to knot invariants.
method Investigate -twisted Alexander matrices and their connection to quandle cocycle invariants.
result Show that -twisted Alexander invariants of knot quandles are stronger than those of knot groups.
The paper defines axis systems for link projections and characterizes them for twist knots.
problem Defining and characterizing axis systems for link projections.
method Defined axis systems of link projections and characterized them for twist knots.
result Characterized axis systems of standard projections of twist knots.
We show that if a split link is obtained from a split link in by -Dehn surgery along a trivial knot , then the link is splittable. That is to say, it is impossible to obtain a split link from a split link via a non-trivial twisting. As its corollary, we completely determine when a trivial li…
Formula for twisted Alexander polynomials of torus links.
problem Computing twisted Alexander polynomials for torus links.
method Explicit formula derivation and character variety analysis.
result Locally constant function on character variety.
Single twist can unknot certain knots, study shows.
problem Can a knot be unknotted with a single twist?
method Classical knot invariants, Casson-Gordon invariants, and Heegaard Floer theory.
result Obstructions to unknotting with a single twist exist.
We show that if a knot admits a prime, twist-reduced diagram with at least 4 twist regions and at least 6 crossings per twist region, then every non-trivial Dehn filling of that knot is hyperbolike. A similar statement holds for links. We prove this using two arguments, one geometric and one combinatorial. The combinat…
Bounding twist number of surface links using polynomial coefficients.
problem Bounding the twist number of alternating surface links.
method Introducing a generalized homological Kauffman bracket and applying it to surface link diagrams.
result A bound for the twist number of alternating surface links in terms of polynomial coefficients.
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.
Jones polynomial for twisted torus knots is trivial if and only if the knot is trivial.
problem Computing Jones polynomial for a specific family of links.
method Computed Jones polynomial for links, focusing on .
result Jones polynomial is trivial if and only if the knot is trivial.
New findings on T-links derived from torus links.
problem Difficulty in determining geometric type of T-links.
method Examined T-links obtained by full twists along torus links.
result T-links obtained by full twists are not torus links.
Study Alexander polynomials to detect fibering and genus of hyperbolic links.
problem Detecting fibering and genus of hyperbolic links.
method Apply twisted Alexander polynomials to study fibering and genus.
result Confirm conjecture on torsion polynomial for hyperbolic 2-bridge links.
We consider knots whose diagrams have a high amount of twisting of multiple strands. By encircling twists on multiple strands with unknotted curves, we obtain a link called a generalized augmented link. Dehn filling this link gives the original knot. We classify those generalized augmented links that are Seifert fibere…
Formula for HOMFLY polynomial in link diagrams.
problem Calculating HOMFLY polynomial for link diagrams.
method Introduced a class of link diagrams, including closed braids, and proved a generalized full-twist formula.
result Generalized formula for HOMFLY polynomial in new class of link diagrams.
Defines and calculates signature invariants for twisted linking forms.
problem Studying twisted linking forms of knots and three-manifolds.
method Describes how to define and calculate signature invariants associated to a linking form for , where is a torsion -module.
result Classifies such linking forms up to isometry and Witt equivalence and studies their representability by matrices.
If the twist numbers of a collection of oriented alternating link diagrams are bounded, then the Alexander polynomials of the corresponding links have bounded euclidean Mahler measure (see Definition 1.2). The converse assertion does not hold. Similarly, if a collection of oriented link diagrams, not necessarily altern…
Formula for Alexander polynomial of links with twists.
problem Computing Alexander polynomial of links with twists.
method Using vector space representation of .
result Alexander polynomials stabilize after adding enough twists.
Twisted braidsmath.GT
Paper proves any twisted link can be described as a unique twisted braid.
problem Understanding twisted links and braids.
method Proved using Alexander and Markov Theorems for classical braids and links.
result Any twisted link can be described as the closure of a unique twisted braid.
Knot invariants and quiver stability linked through full twists.
problem Relating knot invariants to quiver stability under twists.
method Using HOMFLY-PT skein relations and linking/unlinking operations on symmetric quivers.
result Full twists on knots correspond to unlinking or linking of augmented symmetric quivers, confirming stable growth in both.
New proof found for Khovanov's assertion about Frobenius algebra twists.
problem Proving the isomorphism between chain complexes of twisted Frobenius algebras and link diagrams.
method Detailed analysis of configurations of circles in each state.
result A new proof of Khovanov's assertion with a detailed analysis of configurations.
We show that if {L_n} is any infinite sequence of links with twist number tau(L_n) and with cyclotomic Jones polynomials of increasing span, then lim sup tau(L_n)=infty. This implies that any infinite sequence of prime alternating links with cyclotomic Jones polynomials must have unbounded hyperbolic volume. The main t…