37 relations: Commutator subgroup, Constant term, Covering space, Euler characteristic, Fitting ideal, Floer homology, If and only if, Incidence matrix, 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.

## 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.

New!!: Alexander polynomial and Commutator subgroup · See more »

## Constant term

In mathematics, a constant term is a term in an algebraic expression that has a value that is constant or cannot change, because it does not contain any modifiable variables.

New!!: Alexander polynomial and Constant term · See more »

## Covering space

In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below.

New!!: Alexander polynomial and Covering space · See more »

## 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.

New!!: Alexander polynomial and Euler characteristic · See more »

## 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.

New!!: Alexander polynomial and Fitting ideal · See more »

## Floer homology

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

New!!: Alexander polynomial and Floer homology · See more »

## If and only if

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

New!!: Alexander polynomial and If and only if · See more »

## Incidence matrix

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

New!!: Alexander polynomial and Incidence matrix · See more »

## 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.

New!!: Alexander polynomial and James Waddell Alexander II · See more »

## 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 braid theory and knot theory.

New!!: Alexander polynomial and Joan Birman · See more »

## John Horton Conway

John Horton Conway FRS (born 26 December 1937) is an English mathematician active in the theory of finite groups, knot theory, number theory, combinatorial game theory and coding theory.

New!!: Alexander polynomial and John Horton Conway · See more »

## Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984.

New!!: Alexander polynomial and Jones polynomial · See more »

## Knot (mathematics)

In mathematics, a knot is an embedding of a circle S^1 in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

New!!: Alexander polynomial and Knot (mathematics) · See more »

## Knot complement

In mathematics, the knot complement of a tame knot K is the three-dimensional space surrounding the knot.

New!!: Alexander polynomial and Knot complement · See more »

## 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.

New!!: Alexander polynomial and Knot invariant · See more »

## 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.

New!!: Alexander polynomial and Knot polynomial · See more »

## Knot theory

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

New!!: Alexander polynomial and Knot theory · See more »

## 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.

New!!: Alexander polynomial and Laurent polynomial · See more »

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

New!!: Alexander polynomial and Mathematics · See more »

## Michael Freedman

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

New!!: Alexander polynomial and Michael Freedman · See more »

## Module (mathematics)

In mathematics, a module is one of the fundamental algebraic structures used in abstract algebra.

New!!: Alexander polynomial and Module (mathematics) · See more »

## 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.

New!!: Alexander polynomial and Monodromy · See more »

## Orientability

In mathematics, orientability is a property of surfaces in Euclidean space that measures whether it is possible to make a consistent choice of surface normal vector at every point.

New!!: Alexander polynomial and Orientability · See more »

## Perfect group

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

New!!: Alexander polynomial and Perfect group · See more »

## 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.

New!!: Alexander polynomial and Poincaré duality · See more »

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

New!!: Alexander polynomial and Polynomial · See more »

## Principal ideal

In the mathematical field of 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 of P, which is to say the set of all elements less than or equal to x in P. The remainder of this article addresses the ring-theoretic concept.

New!!: Alexander polynomial and Principal ideal · See more »

## Ralph Fox

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

New!!: Alexander polynomial and Ralph Fox · See more »

## 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.

New!!: Alexander polynomial and Satellite knot · See more »

## Seiberg–Witten invariants

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

New!!: Alexander polynomial and Seiberg–Witten invariants · See more »

## Seifert surface

In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is a surface whose boundary is a given knot or link.

New!!: Alexander polynomial and Seifert surface · See more »

## Skein relation

Skein relations are a mathematical tool used to study knots.

New!!: Alexander polynomial and Skein relation · See more »

## Slice knot

A slice knot is a type of mathematical knot.

New!!: Alexander polynomial and Slice knot · See more »

## 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.

New!!: Alexander polynomial and Surgery theory · See more »

## 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.

New!!: Alexander polynomial and Transactions of the American Mathematical Society · See more »

## 3-sphere

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

New!!: Alexander polynomial and 3-sphere · See more »

## 4-manifold

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

New!!: Alexander polynomial and 4-manifold · See more »

## Redirects here:

Alexander invariant, Alexander invariants, Alexander-Conway Polynomial, Alexander-Conway polynomial, Alexander–Conway polynomial, Conway-Alexander polynomial, Skein module.

## References

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