In this paper, we define the primitive/Seifert-fibered property for a knot in S^3. If satisfied, the property ensures that the knot has a Dehn surgery that yields a small Seifert-fibered space (i.e. base S^2 and three or fewer critical fibers). Next we describe the twisted torus knots, which provide an abundance of exa…
On-device research index
arXiv research
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.
168,742 papers · 148 categories
Trend · papers per month
48 results for “small twists knots”
We conjecture formulae of the colored superpolynomials for a class of twist knots where p denotes the number of full twists. The validity of the formulae is checked by applying differentials and taking special limits. Using the formulae, we compute both the classical and quantum super-A-polynomial for the twist k…
Study on the ribbonlength of knots and links, improving upper bounds.
problem Finding the infimal folded ribbonlength of knots and links.
method Creating new folded ribbon knots and applying them to improve upper bounds.
result Improved upper bounds for -torus links, twist knots, and pretzel links.
We describe a simple fundamental domain for the holonomy group of the boundary unipotent spherical CR uniformization of the figure eight knot complement, and deduce that small deformations of that holonomy group (such that the boundary holonomy remains parabolic) also give a uniformization of the figure eight knot comp…
Paper shows how to embed Möbius bands with many twists and small aspect ratios.
problem Finding the smallest aspect ratio for Möbius bands with many twists.
method Constructs a folded paper ribbon knot to bound the aspect ratio.
result Paper Möbius bands and annuli with any number of half-twists can be embedded with aspect ratio less than 8.
We describe a procedure that creates an explicit complex-valued polynomial function of three-dimensional space, whose nodal lines are the three-twist knot . The construction generalizes a similar approach for lemniscate knots: a braid representation is engineered from finite Fourier series and then considered as t…
New infinite families of twisted torus knots found.
problem Identifying new types of twisted torus knots.
method Finding new infinite families of twisted torus knots with a single negative twist.
result Eight new infinite families of twisted torus knots are discovered.
Study shows bounds on volumes of weakly generalised alternating knots.
problem Volume bounds for weakly generalised alternating knots.
method Analysis of weakly generalised alternating knots in 3-manifolds.
result Upper volume bound does not hold for weakly generalised alternating knots.
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.
Formula for Alexander polynomial of twisted torus knots derived.
problem Calculating Alexander polynomial for a specific class of knots.
method Knot group presentation combined with Fox's calculus.
result Explicit formula for Alexander polynomial of twisted torus knots.
Paper shows how to twist knots to make them trivial or non-trivial.
problem Understanding the behavior of knots under twist-spinning operations.
method Analyzes the effect of - and -twist-spinning on classical knots.
result Shows conditions for a knot to be trivial or non-trivial after certain twist-spinning operations.
New families of twisted torus knots found with essential surfaces.
problem Whether all twisted torus knots have essential tori.
method Analyzing sequences of twists on torus knots.
result Found two new families of toroidal twisted torus knots.
Study lattice paths from twist knots and double twist knots.
problem Understanding combinatorics of twist knots and double twist knots.
method Analyzing quiver generating series of HOMFLY-PT polynomial limits.
result Lattice path models for twist knots and double twist knots.
A twisted torus knot is a knot obtained from a torus knot by twisting adjacent strands by full twists. The twisted torus knots lie in , the genus 2 Heegaard surface for . Primitive/primitive and primitive/Seifert knots lie in in a particular way. Dean gives sufficient conditions for the parameters of the tw…
Lee's work on twisted torus knots with Fibonacci parameters is extended to Horadam parameters.
problem Classifying twisted torus knots with Horadam parameters.
method Using recursive Horadam parameters to generalize Lee's work on Fibonacci parameters.
result Families of twisted torus knots with Horadam parameters are provided.
Study finds infinite non-fibered twisted torus knots.
problem Identifying non-fibered twisted torus knots.
method Explicit formula for Alexander polynomial, leading coefficients analysis.
result Infinite families of non-fibered twisted torus knots found.
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.
In this paper, we generalize a result of Satoh to show that for any odd natural , the connected sum of the -twist spun sphere of a knot and an unknotted projective plane in the 4-sphere is equivalent to the same unknotted projective plane. We additionally provide a fix to a small error in Satoh's proof of the…
Positive braids with at least two twists form hyperbolic knots.
problem Classifying knots formed by specific braids.
method Conditions on positive braids with at least two full twists.
result Closure of such braids forms hyperbolic knots.
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.
The paper calculates knot invariants using Blanchfield forms and obstructs sliceness.
problem Computing and obstructing the sliceness of knots.
method Algorithmic computation of twisted signature invariants using twisted Blanchfield forms and satellite formulas.
result Illustrated algorithm for -torus knots and obstruction of sliceness for certain knots.
Knot Floer homology stabilizes with twists.
problem Understanding knot behavior through homology.
method Analyzing full twists on parallel strands.
result Knot Floer homologies stabilize as twists increase.
Study proves bridge and braid indices match for twist positive knots.
problem Determining when bridge and braid indices are equal for knots.
method Used knot Floer torsion order to prove for all twist positive knots.
result Bridge and braid indices coincide for all twist positive knots.
Proved colored HOMFLY-PT polynomials for specific knots.
problem Calculating colored HOMFLY-PT polynomials for specific knots.
method Rigorous mathematical proof for trefoil, figure-eight, and twist knots.
result Colored HOMFLY-PT polynomials expressed as sums for different knots.
Morifuji computed the twisted Alexander polynomial of twist knots for nonabelian representations. In this paper we compute the twisted Alexander polynomial and the Reidemeister torsion of genus one two-bridge knots, a class of knots which includes twist knots. As an application, we give a formula for the Reidemeister t…
The paper studies twisted Alexander polynomials for knot groups in various extensions.
problem Understanding twisted Alexander polynomials in knot groups for different extensions.
method Developed mod p formula for twisted Alexander polynomials and studied central extensions.
result Established formulas for twisted Alexander polynomials in knot groups for various extensions.
The study connects twist positivity to L-space knots and concordance.
problem Understanding the relationship between twist positivity and knot concordance.
method Analyzing Alexander polynomials and braid indices of knots.
result For twist positive L-space knots, the braid index equals the bridge index.
The stable crossing number of a twist family of knots and the satellite crossing number conjecturemath.GT
The paper studies knots formed by twisting a circle around a base knot and conjectures a linear growth in crossing numbers.
problem Understanding the growth rate of crossing numbers in twist families of knots.
method Introduced the stable crossing number and used geometric wrapping and algebraic winding to establish conjectures.
result The crossing number of grows like as for coherent twist families.
New invariant measures how many twists are needed to unknot welded knots.
problem Measuring complexity of welded knots.
method Local twist move, Alexander quandle coloring, Gordian distance.
result Established lower bound on twist number and related it to other knot invariants.
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.
Study on unknotting twisted knots using arc shift and region arc shift moves.
problem Unknotting twisted knots and finding bounds for region arc shift number.
method Introduced arc shift move and region arc shift move for twisted knots.
result Found families of twisted knots with specific arc shift and region arc shift numbers.
The twisted torus knots lie on the standard genus 2 Heegaard surface for , as do the primitive/primitive and primitive/Seifert knots. It is known that primitive/primitive knots are fibered, and that not all primitive/Seifert knots are fibered. Since there is a wealth of primitive/Seifert knots that are twisted tor…
New method distinguishes knots and knotted surfaces.
problem Distinguishing knots and knotted surfaces.
method Twisted set-theoretic Yang-Baxter solutions and Alexander numbering.
result Distinguished -twist spun trefoil from its reverse.
This thesis develops some general calculational techniques for finding the orders of knots in the topological concordance group C. The techniques currently available in the literature are either too theoretical, applying to only a small number of knots, or are designed to only deal with a specific knot. The thesis buil…
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.
Paper calculates the ribbonlength of twisted torus knots.
problem Determining the ribbonlength of twisted torus knots.
method Analyzes the ribbonlength of twisted torus knots and provides upper bounds.
result Ribbonlength of is bounded by and under specific conditions.
New 2-knots found with same knot group but different quandles.
problem Identifying 2-knots with identical knot groups but distinct quandles.
method Analyzing knot quandles of twist spins.
result First example of 2-knots with same knot group but different quandles.
Proves volume conjecture for twist knots using complex analysis.
problem Volume conjecture for twist knots.
method Equivalence relation, complex analysis, analytic continuation, function of several complex variables.
result Proves volume conjecture for twist knots.
This paper extends danceability concept to twisted virtual knots.
problem Danceability of knot diagrams on non-orientable surfaces.
method Expanding danceability concept to twisted virtual knot diagrams.
result Danceability properties of twisted virtual knots.
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.
We calculate the twisted Alexander polynomial with the adjoint action for torus knots and twist knots. As consequences of these calculations, we obtain the formula for the nonabelian Reidemeister torsion of torus knots in \cite{Du} and a formula for the nonabelian Reidemeister torsion of twist knots that is better than…
The twisting number of a ribbon knot is at least as large as its doubly slice genus.
problem Proving a lower bound for the twisting number of ribbon knots in terms of their doubly slice genus.
method Analyzing symmetric unions and tangle replacements to establish the bound.
result Ribbon knots have arbitrarily high twisting numbers, matching their doubly slice genus.
Characterizes groups of branched twist-spun knots.
problem Understanding the groups of branched twist-spun knots.
method Characterization through 3-manifold groups and conjectural algebraic approach.
result Each group is the group of at most finitely many branched twist spins.
Proves bounds on ribbonlength for various knot types.
problem Finding bounds on the infimal folded ribbonlength of knot types.
method Applied techniques to multi-twist Möbius bands and knot constructions.
result Established bounds for torus knots and twist knots.
Study calculates twisted Alexander polynomials for Montesinos knots.
problem Tackles the calculation of twisted Alexander polynomials for Montesinos knots.
method Uses -representations to calculate leading coefficients and degrees of the polynomials.
result Obtains non-monic twisted Alexander polynomials for some nonfibered knots.
Conjectures on the Khovanov Homology of Torus Knots, Twist Knots, and Legendrian Simple Knotsmath.GT
The paper conjectures Khovanov homology can distinguish torus and twist knots.
problem Detecting and distinguishing knots using Khovanov homology.
method Examining all prime knots with up to 20 crossings, conjecturing Legendrian simplicity.
result Numerical evidence supports Khovanov homology distinguishing torus and twist knots.
Innovative warping labeling for twisted knots and braids.
problem Inventing an invariant for twisted knots and braids.
method Introducing warping degree, constructing warping labeling, extending to virtual braids.
result Developed invariants for twisted knots and braids using warping labeling.
The paper studies twisted signature invariants of fibered knots and 3-manifolds.
problem Computing twisted signature invariants of fibered knots and 3-manifolds.
method Reduction to the study of the intersection form and monodromy on the twisted homology of the fiber surface. Use of rings of power series to interpret the twisted Milnor pairing and relate it to twisted Blanchfield pairings.
result New twisted generalizations of the Levine-Tristram signature are derived.