New method proves Jones Polynomial's connect sum property.
problem Jones Polynomial's behavior under connect sums.
method Trip matrix method for calculating Jones Polynomial.
result Jones Polynomial is multiplicative under connect sums.
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48 results for “Jones's method”
This paper will be an exposition of the Kauffman bracket polynomial model of the Jones polynomial, tangle methods for computing the Jones polynomial, and the use of these methods to produce non-trivial links that cannot be detected by the Jones polynomial.
Using a simple recurrence relation we give a new method to compute Jones polynomials of closed braids: we find a general expansion formula and a rational generating function for Jones polynomials. The method is used to estimate degree of Jones polynomials for some families of braids and to obtain general qualitative re…
Proves conjecture for hyperbolic-by-cyclic groups using geometric methods.
problem Proving Farrell-Jones Conjecture for specific group structures.
method Geometric methods and structure theory of mapping tori.
result Proved Farrell-Jones Conjecture for mapping tori of automorphisms of hyperbolic-by-cyclic groups.
We prove the Farrell-Jones conjecture for free-by-cyclic groups. The proof uses recently developed geometric methods for establishing the Farrell-Jones Conjecture.
A state generating is introduced to determine the Jones polynomial of a link. Formulae for two infinite families of knots are shown by applying this method, the second family of which are proved to be non-alternating. Moreover, the method is generalized to compute the Jones-Kauffman polynomial of a virtual link. As exa…
Paper proves knots satisfy a conjecture using Jones polynomial.
problem Proving infinite families of knots satisfy the Cosmetic Surgery Conjecture.
method Computed Jones polynomial and invariants for two knot families.
result Two infinite families of knots satisfy the Purely Cosmetic Surgery Conjecture.
New methods assess topological entanglement in periodic systems.
problem Assessing topological entanglement in systems with periodic boundary conditions.
method Introducing Periodic Jones polynomial and Cell Jones polynomial.
result Periodic Jones polynomial is a recurring factor of Jones polynomial of finite cutoffs.
Evaluating the Jones polynomial with tensor networkscond-mat.stat-mech
We introduce tensor network contraction algorithms for the evaluation of the Jones polynomial of arbitrary knots. The value of the Jones polynomial of a knot maps to the partition function of a -state Potts model defined as a planar graph with weighted edges that corresponds to the knot. For any integer , we cast…
In this paper, a method is given to calculate the Jones polynomial of the 6-plat presentations of knots by using a representation of the braid group into a group of matrices. We also can calculate the Jones polynomial of the -plat presentations of knots by generalizing the method for the …
Verifies knot conjecture for 24-crossing knots.
problem Jones Unknot Conjecture for knots up to 24 crossings.
method Described method of verification with complexity analysis.
result Jones Unknot Conjecture verified for 24 crossings.
New method analyzes Jones polynomial manifold structure.
problem Understanding the structure of Jones polynomial.
method Filtrations and Principal Component Analysis for infinite data sets.
result Jones polynomial can be viewed as an approximately 3 dimensional manifold.
New methods reveal colored Jones polynomials from quantum R-matrices and knot invariants.
problem Understanding colored Jones polynomials of knots.
method Two realizations: quantum R-matrices and refined quantum modularity conjecture.
result New insights into knot invariants from quantum R-matrices and matrix conjectures.
In this note, I will discuss a possible relation between the Mahler measure of the colored Jones polynomial and the volume conjecture. In particular, I will study the colored Jones polynomial of the figure-eight knot on the unit circle. I will also propose a method to prove the volume conjecture for satellites of the f…
Paper extends Cohen's method to compute Jones polynomial for certain braid subfamilies.
problem Computing Jones polynomial for specific knot families.
method Using weighted adjacency matrices and determinants for certain subfamilies of braid groups.
result Jones polynomial can be computed in polynomial time for certain subfamilies of braid groups.
We prove the Farrell-Jones Conjecture for algebraic K-theory of spaces for virtually poly-Z-groups. For this, we transfer the 'Farrell-Hsiang method' from the linear case to categories of equivariant, controlled retractive spaces.
The Jones polynomial and functions of positive type on the oriented Jones-Thompson groups and math.GR
The pioneering work of Jones and Kauffman unveiled a fruitful relationship between statistical mechanics and knot theory. Recently, Jones introduced two subgroups and of the Thompson groups and , respectively, together with a procedure that associates an oriented link diagram to any element o…
The paper characterizes Conway-Coxeter friezes using rational links.
problem Characterizing Conway-Coxeter friezes of zigzag type.
method Characterization via rational links and application to Jones polynomial.
result Jones polynomial can be defined for Conway-Coxeter friezes of zigzag type.
Jones slopes detect figure eight knot, and characterize alternating knots.
problem Detecting knots using Jones polynomials.
method Strong slope conjecture and colored Jones polynomials.
result Jones slopes detect figure eight knot and characterize alternating knots.
Jones polynomials derived from K-theory of a cluster algebra.
problem Jones polynomials of knots and links.
method K-theory of a cluster C*-algebra of the sphere with two cusps.
result Interplay between Chebyshev and Jones polynomials.
The colored Jones polynomial is a knot invariant that plays a central role in low dimensional topology. We give a simple and an efficient algorithm to compute the colored Jones polynomial of any knot. Our algorithm utilizes the walks along a braid model of the colored Jones polynomial that was refined by Armond from th…
Upper bound on Jones polynomials density modulo primes.
problem Density of Jones polynomials modulo prime numbers.
method Derived an upper bound on Jones polynomials density within a large degree range.
result Upper bound on Jones polynomials density modulo primes.
Researchers compute and predict knot volumes using colored Jones polynomials.
problem Computing and predicting volumes of hyperbolic knots.
method Vertex model approach, neural network training, polynomial evaluations.
result 3-colored Jones polynomials predict knot volumes with high accuracy.
Survey on categorifying Jones polynomial.
problem Categorification of Jones polynomial.
method Not explicitly stated, likely involves algebraic and geometric categorification techniques.
result Significance and ramifications in geometry, algebra, and topology.
New formula recovers degree of colored Jones polynomials for pretzel knots.
problem Determining the degree of colored Jones polynomials for specific knots.
method Alternate expansion of the colored Jones polynomial for pretzel links, focusing on 3-tangle knots.
result Determined the degrees of the colored Jones polynomials for a new family of 3-tangle pretzel knots.
Jones constructs knots from Thompson group elements.
problem No specific problem stated; focuses on constructions.
method Constructions of knots from Thompson group elements.
result Introduced two types of knots: oriented and unoriented.
New bound on Jones polynomial for specific positive links.
problem Finding bounds on the Jones polynomial for positive links.
method Using previous results on positive fibered links, we found a new bound for a specific family of positive links.
result We provided a bound on the maximum degree of the Jones polynomial for positive links with a specific coefficient.
Introduction 1. The two-eigenvalue problem 2. Hecke algebra representations of braid groups 3. Duality of Jones-Wenzl representations 4. Closed images of Jones-Wenzl sectors 5. Distribution of evaluations of Jones polynomials 6. Fibonacci representations
We compare three network portfolio selection methods; hierarchical clustering trees, minimum spanning trees and neighbor-Nets, with random and industry group selection methods on twelve years of data from the 30 Dow Jones Industrial Average stocks from 2001 to 2013 for very small private investor sized portfolios. We f…
Jones rational coincidencesmath.GT
Jones polynomial coincidences explored for rational knots.
problem Identifying coincidences in Jones polynomial of rational knots.
method Moves on continued fraction expansion of rational knots, conjectured to generate all coincidences.
result Conjectured moves are sufficient to generate all Jones rational coincidences.
Categorifies Jones polynomial using Lie theory.
problem Categorifying the coloured Jones polynomial.
method Lie theoretic categorification with Jones-Wenzl projectors.
result Constructs a categorification of the coloured Jones polynomial.
We generalize categorified Jones-Wenzl projectors in odd Khovanov homology.
problem Categorify Jones-Wenzl projectors for odd Khovanov homology.
method Develop grading multicategories to replace grading categories, proving existence and uniqueness of categorified projectors.
result Existence and uniqueness of categorified Jones-Wenzl projectors in odd Khovanov homology.
New proof limits Jones polynomial values for quasi-alternating links.
problem Limits on Jones polynomial values for quasi-alternating links.
method Proved finitely many values of Jones polynomial for quasi-alternating links of a given determinant.
result Only finitely many quasi-alternating links have a given Jones polynomial.
The work of Jonesmath.GT
Jones Polynomial shows unity in math.
problem No specific problem stated.
method Discussion of Jones Polynomial.
result Illustrates unity between different mathematical fields.
Paper explores the Jones polynomial and its impact on knot theory and related fields.
problem Exploring the Jones polynomial and its applications in knot theory.
method Recalling the Jones polynomial and its development, discussing its connections to various mathematical and physical contexts.
result The Jones polynomial has wide-ranging applications and connections in mathematics and physics.
The Volume conjecture claims that the hyperbolic Volume of a knot is determined by the colored Jones polynomial. The purpose of this article is to show a Volume-ish theorem for alternating knots in terms of the Jones polynomial, rather than the colored Jones polynomial: The ratio of the Volume and certain sums of coeff…
We show that the Mahler measures of the Jones polynomial and of the colored Jones polynomials converge under twisting for any link. Moreover, almost all of the roots of these polynomials approach the unit circle under twisting. In terms of Mahler measure convergence, the Jones polynomial behaves like hyperbolic volume …
Paper connects AJ conjecture and colored Jones polynomial potential function.
problem Relationship between -polynomial and colored Jones polynomial.
method Connects AJ conjecture and colored Jones polynomial potential function.
result Establishes connection between -polynomial and colored Jones polynomial potential function.
Jones polynomials for knots and links with many crossings calculated efficiently.
problem Computing Jones polynomials for knots and links with a large number of crossings.
method Calculating Tutte polynomials for associated graphs and evaluating with specific substitutions.
result Jones polynomials for knots and links with many crossings calculated efficiently.
An elementary introduction to Khovanov construction of superpolynomials. Despite its technical complexity, this method remains the only source of a definition of superpolynomials from the first principles and therefore is important for development and testing of alternative approaches. In this first part of the review …
A new knot invariant uses permutations to extend Jones polynomials.
problem Extending Jones polynomials to classical and virtual knots and links.
method Colorings by permutations of a finite set to define new knot invariants.
result Established properties and computed polynomials for small cases.
The Jones unknot conjecture states that the Jones polynomial distinguishes the unknot from nontrivial knots. We prove it for knots up to 23 crossings.
Novel Jones polynomial for open curves in 3D space.
problem Measuring entanglement complexity of open curves in 3-space.
method Defining Jones polynomial for linkoids and extending to collections of open and closed curves.
result Jones polynomial for open curves has real coefficients and is continuous.
Paper defines new versions of Jones polynomial and Khovanov homology.
problem No specific problem stated; focuses on new definitions.
method Using maps from Gauss diagrams to their variants to define new Jones polynomial and Khovanov homology.
result New versions of Jones polynomial and Khovanov homology behave differently from original ones.
We describe in this talk three methods of constructing different links with the same Jones type invariant. All three can be thought as generalizations of mutation. The first combines the satellite construction with mutation. The second uses the notion of rotant, taken from the graph theory, the third, invented by Jones…
Study shows quantum modularity in figure-eight knot's colored Jones polynomial.
problem Asymptotic behavior of colored Jones polynomial of figure-eight knot.
method Analyzing polynomial evaluated at specific points and showing asymptotic equivalence.
result Quantum modularity demonstrated in the figure-eight knot's colored Jones polynomial.
The Jones polynomial of a knot in 3-space is a Laurent polynomial in , with integer coefficients. Many people have pondered why is this so, and what is a proper generalization of the Jones polynomial for knots in other closed 3-manifolds. Our paper centers around this question. After reviewing several existing defin…
This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false thet…