Diagram algebras | Polynomials | Knot invariants | Knot theory

Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a version of this polynomial, now called the Alexander–Conway polynomial, could be computed using a skein relation, although its significance was not realized until the discovery of the Jones polynomial in 1984. Soon after Conway's reworking of the Alexander polynomial, it was realized that a similar skein relation was exhibited in Alexander's paper on his polynomial. (Wikipedia).

Alexander polynomial
Video thumbnail

Classify a polynomial then determining if it is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Is it a polynomial with two variables

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Determining if a equation is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Learn how to identify if a function is a polynomial and identify the degree and LC

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Determining if a function is a polynomial or not then determine degree and LC

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

Video thumbnail

Classifying a polynomial based on its degree and number of terms

👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1

From playlist Classify Polynomials | Equations

Video thumbnail

Summary for classifying polynomials

👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different interger exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1

From playlist Classify Polynomials

Video thumbnail

Is the Conway knot slice? (After Lisa Piccirillo)

This is a talk on the recent work by Lisa Piccirillo showing that the Conway know is not a slice knot. We first review the definitions of the Conway know and slice knots, and then give an overview of her proof. The paper on this by Lisa Piccirillo can be found at https://arxiv.org/pdf/1

From playlist Math talks

Video thumbnail

Max Zahoransky von Worlik: The Alexander Polynomial for Knots in the 3-Torus

Max Zahoransky von Worlik, Technische Universitat Berlin Title: The Alexander Polynomial for Knots in the 3-Torus In this talk I will explain how to obtain diagrammatic representations for knots and links in the 3-torus. This includes a discussion of how one can obtain a complete set of is

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Video thumbnail

Untangling the beautiful math of KNOTS

Visit ► https://brilliant.org/TreforBazett/ to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Suppose yo

From playlist Cool Math Series

Video thumbnail

Labeling a polynomial based on the degree and number of terms

👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1

From playlist Classify Polynomials | Equations

Video thumbnail

Alexandru Dimca: A computational approach to Milnor fiber cohomology

Abstract: In this talk we consider the Milnor fiber F associated to a reduced projective plane curve C. A computational approach for the determination of the characteristic polynomial of the monodromy action on the first cohomology group of F, also known as the Alexander polynomial of the

From playlist Algebraic and Complex Geometry

Video thumbnail

Heegaard Biagrams and Holomorphic Disks - Peter Ozsváth

75th Anniversary Celebration School of Mathematics Peter Ozsváth Columbia University March 12, 2005 More videos on http://video.ias.edu

From playlist Mathematics

Video thumbnail

Becca Winarski: Characterizing Thurston maps by lifting trees

HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 23, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Luca Récanzone Find this video and other talks given by worldwide mathematicians on CIRM's Audi

From playlist Topology

Video thumbnail

Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality

The Alexandrov-Fenchel inequality is a far-reaching generalization of the classical isoperimetric inequality to arbitrary mixed volumes. It is one of the central results in convex geometry, and has deep connections with other areas of mathematics. The characterization of its extremal bodie

From playlist Trimester Seminar Series on the Interplay between High-Dimensional Geometry and Probability

Video thumbnail

Charles Stine: The Complexity of Shake Slice Knots

Charles Stine, Brandeis University Title: The Complexity of Shake Slice Knots It is a well studied conjecture that a shake slice knot is in fact slice. Many counterexamples have been given, but most are close to being slice in a technical sense. In this talk, we will give a precise way to

From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022

Video thumbnail

Ian Zemke - Concordance surgery and the Ozsváth--Szabó 4-manifold invariant

June 29, 2018 - This talk was part of the 2018 RTG mini-conference Low-dimensional topology and its interactions with symplectic geometry

From playlist 2018 RTG mini-conference on low-dimensional topology and its interactions with symplectic geometry II

Video thumbnail

Classify a polynomial and determine degree and leading coefficient

👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1

From playlist Classify Polynomials | Equations

Video thumbnail

Classify a polynomial and determine degree and leading coefficient

👉 Learn how to classify polynomials. A polynomial is an expression of the sums/differences of two or more terms having different integer exponents of the same variable. A polynomial can be classified in two ways: by the number of terms and by its degree. A monomial is an expression of 1

From playlist Classify Polynomials | Equations

Related pages

Monodromy | 3-sphere | Jones polynomial | If and only if | Knot polynomial | Surgery theory | Satellite knot | John Horton Conway | Knot (mathematics) | Knot invariant | Polynomial | Euler characteristic | Incidence matrix | Poincaré duality | Skein relation | Mathematics | Laurent polynomial | Floer homology | Constant term | Perfect group | Covering space | Commutator subgroup | Seifert surface | Fitting ideal | Knot complement | Principal ideal | Module (mathematics) | 4-manifold | Knot theory