We are working to restore the Unionpedia app on the Google Play Store
OutgoingIncoming
🌟We've simplified our design for better navigation!
Instagram Facebook X LinkedIn
Your own Unionpedia with your logo and domain, from 9.99 USD/month
Create my Unionpedia

Alexander polynomial

Index Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. [1]

Table of Contents

  1. 40 relations: Advances in Mathematics, Commutator subgroup, Constant term, Covering space, Euler characteristic, Fitting ideal, Floer homology, Geometry & Topology, If and only if, Incidence matrix, Inventiones Mathematicae, James Waddell Alexander II, Joan Birman, John Horton Conway, Jones polynomial, Knot (mathematics), Knot complement, Knot invariant, Knot polynomial, Knot theory, Laurent polynomial, Mathematics, Michael Freedman, Module (mathematics), Monodromy, Orientability, Perfect group, Poincaré duality, Polynomial, Principal ideal, Ralph Fox, Satellite knot, Seiberg–Witten invariants, Seifert surface, Skein relation, Slice knot, Surgery theory, Transactions of the American Mathematical Society, 3-sphere, 4-manifold.

  2. Diagram algebras
  3. John Horton Conway
  4. Knot invariants

Advances in Mathematics

Advances in Mathematics is a peer-reviewed scientific journal covering research on pure mathematics.

See Alexander polynomial and Advances in Mathematics

Commutator subgroup

In mathematics, more specifically in abstract algebra, the commutator subgroup or derived subgroup of a group is the subgroup generated by all the commutators of the group.

See Alexander polynomial and Commutator subgroup

Constant term

In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. Alexander polynomial and constant term are polynomials.

See Alexander polynomial and Constant term

Covering space

In topology, a covering or covering projection is a map between topological spaces that, intuitively, locally acts like a projection of multiple copies of a space onto itself.

See Alexander polynomial and Covering space

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 Alexander polynomial and Euler characteristic

Fitting ideal

In commutative algebra, the Fitting ideals of a finitely generated module over a commutative ring describe the obstructions to generating the module by a given number of elements.

See Alexander polynomial and Fitting ideal

Floer homology

In mathematics, Floer homology is a tool for studying symplectic geometry and low-dimensional topology.

See Alexander polynomial and Floer homology

Geometry & Topology

Geometry & Topology is a peer-refereed, international mathematics research journal devoted to geometry and topology, and their applications.

See Alexander polynomial and Geometry & Topology

If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements.

See Alexander polynomial and If and only if

Incidence matrix

In mathematics, an incidence matrix is a logical matrix that shows the relationship between two classes of objects, usually called an incidence relation.

See Alexander polynomial and Incidence matrix

Inventiones Mathematicae

Inventiones Mathematicae is a mathematical journal published monthly by Springer Science+Business Media.

See Alexander polynomial and Inventiones Mathematicae

James Waddell Alexander II

James Waddell Alexander II (September 19, 1888 September 23, 1971) was a mathematician and topologist of the pre-World War II era and part of an influential Princeton topology elite, which included Oswald Veblen, Solomon Lefschetz, and others.

See Alexander polynomial and James Waddell Alexander II

Joan Birman

Joan Sylvia Lyttle Birman (born May 30, 1927, in New York CityLarry Riddle. "", Biographies of Women Mathematicians, at Agnes Scott College) is an American mathematician, specializing in low-dimensional topology.

See Alexander polynomial and Joan Birman

John Horton Conway

John Horton Conway (26 December 1937 – 11 April 2020) was an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

See Alexander polynomial and John Horton Conway

Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Alexander polynomial and Jones polynomial are knot invariants, knot theory and polynomials.

See Alexander polynomial and Jones polynomial

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 Alexander polynomial and Knot (mathematics)

Knot complement

In mathematics, the knot complement of a tame knot K is the space where the knot is not. Alexander polynomial and knot complement are knot theory.

See Alexander 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. Alexander polynomial and knot invariant are knot invariants.

See Alexander 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. Alexander polynomial and knot polynomial are knot invariants and polynomials.

See Alexander polynomial and Knot polynomial

Knot theory

In topology, knot theory is the study of mathematical knots.

See Alexander polynomial and Knot theory

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. Alexander polynomial and Laurent polynomial are polynomials.

See Alexander polynomial and Laurent polynomial

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Alexander polynomial and Mathematics

Michael Freedman

Michael Hartley Freedman (born April 21, 1951) is an American mathematician at Microsoft Station Q, a research group at the University of California, Santa Barbara.

See Alexander polynomial and Michael Freedman

Module (mathematics)

In mathematics, a module is a generalization of the notion of vector space in which the field of scalars is replaced by a ring.

See Alexander polynomial and Module (mathematics)

Monodromy

In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.

See Alexander polynomial and Monodromy

Orientability

In mathematics, orientability is a property of some topological spaces such as real vector spaces, Euclidean spaces, surfaces, and more generally manifolds that allows a consistent definition of "clockwise" and "anticlockwise".

See Alexander polynomial and Orientability

Perfect group

In mathematics, more specifically in group theory, a group is said to be perfect if it equals its own commutator subgroup, or equivalently, if the group has no non-trivial abelian quotients (equivalently, its abelianization, which is the universal abelian quotient, is trivial).

See Alexander polynomial and Perfect group

Poincaré duality

In mathematics, the Poincaré duality theorem, named after Henri Poincaré, is a basic result on the structure of the homology and cohomology groups of manifolds.

See Alexander polynomial and Poincaré duality

Polynomial

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms. Alexander polynomial and polynomial are polynomials.

See Alexander polynomial and Polynomial

Principal ideal

In mathematics, specifically ring theory, a principal ideal is an ideal I in a ring R that is generated by a single element a of R through multiplication by every element of R. The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset P generated by a single element x \in P, which is to say the set of all elements less than or equal to x in P.

See Alexander polynomial and Principal ideal

Ralph Fox

Ralph Hartzler Fox (March 24, 1913 – December 23, 1973) was an American mathematician.

See Alexander polynomial and Ralph Fox

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. Alexander polynomial and satellite knot are knot theory.

See Alexander polynomial and Satellite knot

Seiberg–Witten invariants

In mathematics, and especially gauge theory, Seiberg–Witten invariants are invariants of compact smooth oriented 4-manifolds introduced by, using the Seiberg–Witten theory studied by during their investigations of Seiberg–Witten gauge theory.

See Alexander polynomial and Seiberg–Witten invariants

Seifert surface

In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link. Alexander polynomial and Seifert surface are knot theory.

See Alexander polynomial and Seifert surface

Skein relation

Skein relations are a mathematical tool used to study knots. Alexander polynomial and Skein relation are Diagram algebras and knot theory.

See Alexander polynomial and Skein relation

Slice knot

A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space.

See Alexander polynomial and Slice knot

Surgery theory

In mathematics, specifically in geometric topology, surgery theory is a collection of techniques used to produce one finite-dimensional manifold from another in a 'controlled' way, introduced by.

See Alexander polynomial and Surgery theory

Transactions of the American Mathematical Society

The Transactions of the American Mathematical Society is a monthly peer-reviewed scientific journal of mathematics published by the American Mathematical Society.

See Alexander polynomial and Transactions of the American Mathematical Society

3-sphere

In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere.

See Alexander polynomial and 3-sphere

4-manifold

In mathematics, a 4-manifold is a 4-dimensional topological manifold.

See Alexander polynomial and 4-manifold

See also

Diagram algebras

John Horton Conway

Knot invariants

References

[1] https://en.wikipedia.org/wiki/Alexander_polynomial

Also known as Alexander invariant, Alexander invariants, Alexander-Conway Polynomial, Conway-Alexander polynomial, Skein module.