scholarly journals A New Point of View in the Theory of Knot and Link Invariants

2002 ◽  
Vol 11 (02) ◽  
pp. 173-197 ◽  
Author(s):  
José M. F. Labastida ◽  
Marcos Mariño
Keyword(s):  
Quantum Group ◽  
Riemann Surfaces ◽  
Recent Progress ◽  
General Structure ◽  
Point Of View ◽  
Enumerative Geometry ◽  
Geometrical Meaning ◽  
Polynomial Invariants ◽  
Link Invariants ◽  
Knots And Links

Recent progress in string theory has led to a reformulation of quantum-group polynomial invariants for knots and links into new polynomial invariants whose coefficients can be understood in topological terms. We describe in detail how to construct the new polynomials and we conjecture their general structure. This leads to new conjectures on the algebraic structure of the quantum-group polynomial invariants. We also describe the geometrical meaning of the coefficients in terms of the enumerative geometry of Riemann surfaces with boundaries in a certain Calabi-Yau threefold.

MULTI-VARIABLE POLYNOMIAL INVARIANTS FOR VIRTUAL LINKS

2003 ◽  
Vol 12 (08) ◽  
pp. 1131-1144 ◽  
Author(s):  
VASSILY O. MANTUROV
Keyword(s):  
Virtual Link ◽  
Invariant Polynomials ◽  
Polynomial Invariants ◽  
Link Invariants ◽  
Virtual Knots ◽  
Virtual Links ◽  
Multiple Variables ◽  
Kauffman Polynomial ◽  
Knots And Links

We construct new invariant polynomials in two and multiple variables for virtual knots and links. They are defined as determinants of Alexander-like matrices whose determinants are virtual link invariants. These polynomials vanish on classical links. In some cases, they separate links that can not be separated by the Jones–Kauffman polynomial [Kau] and the polynomial proposed in [Ma3].

Jones polynomial invariants for knots and satellites

1991 ◽  
Vol 109 (1) ◽  
pp. 83-103 ◽  
Author(s):  
H. R. Morton ◽  
P. Strickland
Keyword(s):  
Quantum Group ◽  
Linear Combination ◽  
Simple Formula ◽  
Jones Polynomial ◽  
Polynomial Invariants ◽  
Satellite Link ◽  
Representation Ring ◽  
Parallel Links ◽  
Jones Polynomials ◽  
Special Case

AbstractResults of Kirillov and Reshetikhin on constructing invariants of framed links from the quantum group SU(2)q are adapted to give a simple formula relating the invariants for a satellite link to those of the companion and pattern links used in its construction. The special case of parallel links is treated first. It is shown as a consequence that any SU(2)q-invariant of a link L is a linear combination of Jones polynomials of parallels of L, where the combination is determined explicitly from the representation ring of SU(2). As a simple illustration Yamada's relation between the Jones polynomial of the 2-parallel of L and an evaluation of Kauffman's polynomial for sublinks of L is deduced.

scholarly journals ALL LINK INVARIANTS FOR TWO DIMENSIONAL SOLUTIONS OF YANG–BAXTER EQUATION AND DRESSINGS

2006 ◽  
Vol 15 (10) ◽  
pp. 1279-1301
Author(s):  
N. AIZAWA ◽  
M. HARADA ◽  
M. KAWAGUCHI ◽  
E. OTSUKI
Keyword(s):  
Jones Polynomial ◽  
Alexander Polynomial ◽  
Baxter Equation ◽  
Two Dimensional ◽  
Link Invariant ◽  
Three Solutions ◽  
Polynomial Invariants ◽  
Link Invariants ◽  
Higher Dimensional

All polynomial invariants of links for two dimensional solutions of Yang–Baxter equation is constructed by employing Turaev's method. As a consequence, it is proved that the best invariant so constructed is the Jones polynomial and there exist three solutions connecting to the Alexander polynomial. Invariants for higher dimensional solutions, obtained by the so-called dressings, are also investigated. It is observed that the dressings do not improve link invariant unless some restrictions are put on dressed solutions.

scholarly journals BIRACK SHADOW MODULES AND THEIR LINK INVARIANTS

2013 ◽  
Vol 22 (10) ◽  
pp. 1350056 ◽  
Author(s):  
SAM NELSON ◽  
KATIE PELLAND
Keyword(s):  
Associative Algebra ◽  
Alexander Polynomial ◽  
Link Invariants ◽  
Knots And Links

We introduce an associative algebra ℤ[X, S] associated to a birack shadow and define enhancements of the birack counting invariant for classical knots and links via representations of ℤ[X, S] known as shadow modules. We provide examples which demonstrate that the shadow module enhanced invariants are not determined by the Alexander polynomial or the unenhanced birack counting invariants.

Assessment of Citrus Key Lime Production Supply, Exports and Domestic Demand in Mexico before and through the Threat of Citrus Greening (HLB)

2015 ◽  
Vol 16 (1) ◽  
pp. 36-56
Author(s):  
Maria Elena Vera Villagran ◽  
L. Myriam Sagarnaga Villegas ◽  
Jose Salas Gonzalez ◽  
Juan Leos Rodriguez
Keyword(s):  
General Structure ◽  
Supply And Demand ◽  
Point Of View ◽  
Citrus Greening ◽  
Economic Point ◽  
Key Variables ◽  
Key Lime ◽  
The Right ◽  
Lime Production ◽  
The Relationship

This project looks for the relationship among variables influencing Mexican key lime supply and demand in the domestic and US market under the scenario of using a higher quantity of fertilizers as a strategy for responding against the threat of citrus greening (HLB). With the help of domestic and international databases from 2000 to 2012, a simultaneous equations model was built capturing behavioral and technical variables influencing supply and demand. The most important relationships among variables were price of the product and disposable income for the demand and use of fertilizers and exchange rate for the supply. This work gives the insight, from the economic point of view, that building a model including the right key variables will give a sense of the general structure of a market and the changes in stability due to a sanitary threat

scholarly journals Introduction to disoriented knot theory

2018 ◽  
Vol 16 (1) ◽  
pp. 346-357
Author(s):  
İsmet Altıntaş
Keyword(s):  
Knot Theory ◽  
Jones Polynomial ◽  
Polynomial Invariants ◽  
Linking Number ◽  
Link Diagrams ◽  
New Ideas ◽  
Numerical Invariants ◽  
Bracket Polynomial ◽  
Knots And Links

AbstractThis paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot, disoriented crossing and Reidemesiter moves for disoriented diagrams, numerical invariants such as the linking number and the complete writhe, the polynomial invariants such as the bracket polynomial, the Jones polynomial for the disoriented knots and links.

scholarly journals Graph polynomials and link invariants as positive type functions on Thompson’s group F

2019 ◽  
Vol 28 (02) ◽  
pp. 1950006 ◽  
Author(s):  
Valeriano Aiello ◽  
Roberto Conti
Keyword(s):  
Elementary Proof ◽  
Tutte Polynomial ◽  
Positive Type ◽  
Polynomial Invariants ◽  
Graph Polynomials ◽  
Link Invariants ◽  
Kauffman Bracket ◽  
Model Interpretation ◽  
Mechanics Model ◽  
Thompson’S Group

In a recent paper, Jones introduced a correspondence between elements of the Thompson group [Formula: see text] and certain graphs/links. It follows from his work that several polynomial invariants of links, such as the Kauffman bracket, can be reinterpreted as coefficients of certain unitary representations of [Formula: see text]. We give a somewhat different and elementary proof of this fact for the Kauffman bracket evaluated at certain roots of unity by means of a statistical mechanics model interpretation. Moreover, by similar methods we show that, for some particular specializations of the variables, other familiar link invariants and graph polynomials, namely the number of [Formula: see text]-colorings and the Tutte polynomial, can be viewed as positive definite functions on [Formula: see text].

scholarly journals Export Compliance: A Missing Component of International Entrepreneurship

2017 ◽  
Vol 12 (11) ◽  
pp. 103 ◽  
Author(s):  
Vahid Jafari Sadeghi ◽  
Paolo Pietro Biancone ◽  
Charles Giacoma ◽  
Silvana Secinaro
Keyword(s):  
Corporate Governance ◽  
Web Sites ◽  
General Structure ◽  
Point Of View ◽  
The European Union ◽  
Legal Provisions ◽  
The World ◽  
Scientific Research Articles ◽  
Restrictive Measures ◽  
Export Compliance

There is a consensus that firm’s corporate governance impacts their ability to export. Corporate governance relies on export compliance as a framework which supports enterprises in order to mitigate their risks associated with export and provides a safe platform for firms to upgrade their position in the world of trade. The aim of this paper is to widen concepts of export control and compliance framework. The paper outlines the general structure of export compliance and presents a comprehensive view of United States of America and the European Union as powers in the world. In this study, we explained the nature of the violations from the point of view of export compliance and reached to dual-use, money laundering violation and sanctions embargos or restrictive measures. The methodology of this study is documenting analysis with an inductive approach. Essential data for this study has been gathered from secondary resources including diverse scientific research articles, institutional guidance notes, guidelines, manuals and export compliance related web sites and legal provisions in legislations of different countries.

THE HOMFLY POLYNOMIAL FOR TORUS LINKS FROM CHERN–SIMONS GAUGE THEORY

1995 ◽  
Vol 10 (07) ◽  
pp. 1045-1089 ◽  
Author(s):  
J. M. F. LABASTIDA ◽  
M. MARIÑO
Keyword(s):  
Gauge Theory ◽  
Gauge Group ◽  
Homfly Polynomial ◽  
Fundamental Representation ◽  
Torus Knots ◽  
Polynomial Invariants ◽  
Chern Simons ◽  
Knots And Links ◽  
Torus Links

Polynomial invariants corresponding to the fundamental representation of the gauge group SU(N) are computed for arbitrary torus knots and links in the framework of Chern–Simons gauge theory making use of knot operators. As a result, a formula for the HOMFLY polynomial for arbitrary torus links is presented.

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