Table of Contents
56 relations: Alexander polynomial, Alexander's theorem, Alternating polynomial, American Mathematical Society, Annals of Mathematics, Bracket polynomial, Braid group, Bulletin of the American Mathematical Society, Chern–Simons theory, Chiral knot, Chord diagram (mathematics), Communications in Mathematical Physics, Dror Bar-Natan, Edward Witten, Euler characteristic, Finite type invariant, Fundamental representation, Gauge group (mathematics), Hernando Burgos-Soto, HOMFLY polynomial, Hyperbolic volume, Journal of Knot Theory and Its Ramifications, Khovanov homology, Knot (mathematics), Knot complement, Knot invariant, Knot polynomial, Knot theory, Kontsevich invariant, Laurent polynomial, Link (knot theory), Louis Kauffman, Maxim Kontsevich, Mikhail Khovanov, Morwen Thistlethwaite, Palindrome, Potts model, Quantum group, Reidemeister move, Reshetikhin–Turaev invariant, Ring (mathematics), Root of unity, Satellite knot, Skein relation, Statistical mechanics, Tangle (mathematics), Temperley–Lieb algebra, Topology (journal), Unknot, Unlink, ... Expand index (6 more) »
- Knot invariants
Alexander polynomial
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. Jones polynomial and Alexander polynomial are knot invariants, knot theory and polynomials.
See Jones polynomial and Alexander polynomial
Alexander's theorem
In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends of the strings are connected in pairs. Jones polynomial and Alexander's theorem are knot theory.
See Jones polynomial and Alexander's theorem
Alternating polynomial
In algebra, an alternating polynomial is a polynomial f(x_1,\dots,x_n) such that if one switches any two of the variables, the polynomial changes sign: Equivalently, if one permutes the variables, the polynomial changes in value by the sign of the permutation: More generally, a polynomial f(x_1,\dots,x_n,y_1,\dots,y_t) is said to be alternating in x_1,\dots,x_n if it changes sign if one switches any two of the x_i, leaving the y_j fixed. Jones polynomial and alternating polynomial are polynomials.
See Jones polynomial and Alternating polynomial
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, advocacy and other programs.
See Jones polynomial and American Mathematical Society
Annals of Mathematics
The Annals of Mathematics is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study.
See Jones polynomial and Annals of Mathematics
Bracket polynomial
In the mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links. Jones polynomial and bracket polynomial are knot theory and polynomials.
See Jones polynomial and Bracket polynomial
Braid group
In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see); and in monodromy invariants of algebraic geometry. Jones polynomial and braid group are knot theory.
See Jones polynomial and Braid group
Bulletin of the American Mathematical Society
The Bulletin of the American Mathematical Society is a quarterly mathematical journal published by the American Mathematical Society.
See Jones polynomial and Bulletin of the American Mathematical Society
Chern–Simons theory
The Chern–Simons theory is a 3-dimensional topological quantum field theory of Schwarz type developed by Edward Witten.
See Jones polynomial and Chern–Simons theory
Chiral knot
In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed).
See Jones polynomial and Chiral knot
Chord diagram (mathematics)
In mathematics, a chord diagram consists of a cyclic order on a set of objects, together with a one-to-one pairing (perfect matching) of those objects. Jones polynomial and chord diagram (mathematics) are knot theory.
See Jones polynomial and Chord diagram (mathematics)
Communications in Mathematical Physics
Communications in Mathematical Physics is a peer-reviewed academic journal published by Springer.
See Jones polynomial and Communications in Mathematical Physics
Dror Bar-Natan
Dror Bar-Natan (דרוֹר בָר-נָתָן; born January 30, 1966) is a professor at the University of Toronto Department of Mathematics, Canada.
See Jones polynomial and Dror Bar-Natan
Edward Witten
Edward Witten (born August 26, 1951) is an American theoretical physicist known for his contributions to string theory, topological quantum field theory, and various areas of mathematics.
See Jones polynomial and Edward Witten
Euler characteristic
In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.
See Jones polynomial and Euler characteristic
Finite type invariant
In the mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant that can be extended (in a precise manner to be described) to an invariant of certain singular knots that vanishes on singular knots with m + 1 singularities and does not vanish on some singular knot with 'm' singularities. Jones polynomial and finite type invariant are knot invariants.
See Jones polynomial and Finite type invariant
Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight.
See Jones polynomial and Fundamental representation
Gauge group (mathematics)
A gauge group is a group of gauge symmetries of the Yang–Mills gauge theory of principal connections on a principal bundle.
See Jones polynomial and Gauge group (mathematics)
Hernando Burgos-Soto
Hernando Burgos Soto is a Canadian (Colombian born) writer and mathematician, professor of mathematics at George Brown College.
See Jones polynomial and Hernando Burgos-Soto
HOMFLY polynomial
In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant in the form of a polynomial of variables m and l. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. Jones polynomial and HOMFLY polynomial are knot theory and polynomials.
See Jones polynomial and HOMFLY polynomial
Hyperbolic volume
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete hyperbolic metric. Jones polynomial and hyperbolic volume are knot invariants and knot theory.
See Jones polynomial and Hyperbolic volume
Journal of Knot Theory and Its Ramifications
The Journal of Knot Theory and Its Ramifications was established in 1992 by Louis Kauffman and was the first journal purely devoted to knot theory.
See Jones polynomial and Journal of Knot Theory and Its Ramifications
Khovanov homology
In mathematics, Khovanov homology is an oriented link invariant that arises as the cohomology of a cochain complex. Jones polynomial and Khovanov homology are knot invariants.
See Jones polynomial and Khovanov homology
Knot (mathematics)
In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other.
See Jones polynomial and Knot (mathematics)
Knot complement
In mathematics, the knot complement of a tame knot K is the space where the knot is not. Jones polynomial and knot complement are knot theory.
See Jones polynomial and Knot complement
Knot invariant
In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots. Jones polynomial and knot invariant are knot invariants.
See Jones polynomial and Knot invariant
Knot polynomial
In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot. Jones polynomial and knot polynomial are knot invariants and polynomials.
See Jones polynomial and Knot polynomial
Knot theory
In topology, knot theory is the study of mathematical knots.
See Jones polynomial and Knot theory
Kontsevich invariant
In the mathematical theory of knots, the Kontsevich invariant, also known as the Kontsevich integral of an oriented framed link, is a universal Vassiliev invariant in the sense that any coefficient of the Kontsevich invariant is of a finite type, and conversely any finite type invariant can be presented as a linear combination of such coefficients. Jones polynomial and Kontsevich invariant are knot invariants.
See Jones polynomial and Kontsevich invariant
Laurent polynomial
In mathematics, a Laurent polynomial (named after Pierre Alphonse Laurent) in one variable over a field \mathbb is a linear combination of positive and negative powers of the variable with coefficients in \mathbb. Jones polynomial and Laurent polynomial are polynomials.
See Jones polynomial and Laurent polynomial
Link (knot theory)
In mathematical knot theory, a link is a collection of knots which do not intersect, but which may be linked (or knotted) together.
See Jones polynomial and Link (knot theory)
Louis Kauffman
Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, mathematical physicist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago.
See Jones polynomial and Louis Kauffman
Maxim Kontsevich
Maxim Lvovich Kontsevich (Макси́м Льво́вич Конце́вич,; born 25 August 1964) is a Russian and French mathematician and mathematical physicist.
See Jones polynomial and Maxim Kontsevich
Mikhail Khovanov
Mikhail Khovanov (Михаил Гелиевич Хованов; born 1972) is a Russian-American professor of mathematics at Columbia University who works on representation theory, knot theory, and algebraic topology.
See Jones polynomial and Mikhail Khovanov
Morwen Thistlethwaite
Morwen Bernard Thistlethwaite (born 5 June 1945) is a knot theorist and professor of mathematics for the University of Tennessee in Knoxville.
See Jones polynomial and Morwen Thistlethwaite
Palindrome
A palindrome is a word, number, phrase, or other sequence of symbols that reads the same backwards as forwards, such as madam or racecar, the date "22/02/2022" and the sentence: "A man, a plan, a canal – Panama".
See Jones polynomial and Palindrome
Potts model
In statistical mechanics, the Potts model, a generalization of the Ising model, is a model of interacting spins on a crystalline lattice.
See Jones polynomial and Potts model
Quantum group
In mathematics and theoretical physics, the term quantum group denotes one of a few different kinds of noncommutative algebras with additional structure.
See Jones polynomial and Quantum group
Reidemeister move
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram.
See Jones polynomial and Reidemeister move
Reshetikhin–Turaev invariant
In the mathematical field of quantum topology, the Reshetikhin–Turaev invariants (RT-invariants) are a family of quantum invariants of framed links.
See Jones polynomial and Reshetikhin–Turaev invariant
Ring (mathematics)
In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and multiplicative inverses need not exist.
See Jones polynomial and Ring (mathematics)
Root of unity
In mathematics, a root of unity, occasionally called a de Moivre number, is any complex number that yields 1 when raised to some positive integer power. Jones polynomial and root of unity are polynomials.
See Jones polynomial and Root of unity
Satellite knot
In the mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement. Jones polynomial and satellite knot are knot theory.
See Jones polynomial and Satellite knot
Skein relation
Skein relations are a mathematical tool used to study knots. Jones polynomial and Skein relation are knot theory.
See Jones polynomial and Skein relation
Statistical mechanics
In physics, statistical mechanics is a mathematical framework that applies statistical methods and probability theory to large assemblies of microscopic entities.
See Jones polynomial and Statistical mechanics
Tangle (mathematics)
In mathematics, a tangle is generally one of two related concepts. Jones polynomial and tangle (mathematics) are knot theory.
See Jones polynomial and Tangle (mathematics)
Temperley–Lieb algebra
In statistical mechanics, the Temperley–Lieb algebra is an algebra from which are built certain transfer matrices, invented by Neville Temperley and Elliott Lieb. Jones polynomial and Temperley–Lieb algebra are knot theory.
See Jones polynomial and Temperley–Lieb algebra
Topology (journal)
Topology was a peer-reviewed mathematical journal covering topology and geometry.
See Jones polynomial and Topology (journal)
Unknot
In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Jones polynomial and unknot are knot theory.
See Jones polynomial and Unknot
Unlink
In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to finitely many disjoint circles in the plane. Jones polynomial and unlink are knot theory.
See Jones polynomial and Unlink
Vacuum expectation value
In quantum field theory the vacuum expectation value (also called condensate or simply VEV) of an operator is its average or expectation value in the vacuum.
See Jones polynomial and Vacuum expectation value
Vaughan Jones
Sir Vaughan Frederick Randal Jones (31 December 19526 September 2020) was a New Zealand mathematician known for his work on von Neumann algebras and knot polynomials.
See Jones polynomial and Vaughan Jones
Vladimir Turaev
Vladimir Georgievich Turaev (Владимир Георгиевич Тураев, born in 1954) is a Russian mathematician, specializing in topology.
See Jones polynomial and Vladimir Turaev
Volume conjecture
In the branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry of their complements. Jones polynomial and volume conjecture are knot theory.
See Jones polynomial and Volume conjecture
Wilson loop
In quantum field theory, Wilson loops are gauge invariant operators arising from the parallel transport of gauge variables around closed loops.
See Jones polynomial and Wilson loop
Writhe
In knot theory, there are several competing notions of the quantity writhe, or \operatorname. Jones polynomial and writhe are knot theory.
See Jones polynomial and Writhe
See also
Knot invariants
- Alexander polynomial
- Alternating knot
- Arf invariant of a knot
- Bridge number
- Crosscap number
- Crossing number (knot theory)
- Finite type invariant
- Hyperbolic volume
- Jones polynomial
- Khovanov homology
- Knot chirality
- Knot group
- Knot invariant
- Knot polynomial
- Kontsevich invariant
- Link concordance
- Link group
- Linking number
- Prime knot
- Ropelength
- Self-linking number
- Signature of a knot
- Stick number
- Thurston–Bennequin number
- Tricolorability
- Tunnel number
- Unknotting number
References
Also known as Jones function, Jones' polynomials.