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HOMFLY polynomial

Index HOMFLY polynomial

In the mathematical field of knot theory, the HOMFLY polynomial, sometimes called the HOMFLY-PT polynomial or 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. [1]

18 relations: Alexander polynomial, Chirality, Connected sum, Józef H. Przytycki, Jones polynomial, Kenneth Millett, Knot invariant, Knot polynomial, Knot theory, Louis Kauffman, Mathematics, Octacube (sculpture), Peter J. Freyd, Polynomial, Prime knot, Quantum invariant, Skein relation, W. B. R. Lickorish.

Alexander polynomial

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

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Chirality is a property of asymmetry important in several branches of science.

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Connected sum

In mathematics, specifically in topology, the operation of connected sum is a geometric modification on manifolds.

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Józef H. Przytycki

Józef Henryk Przytycki (born October 1953 in Warsaw, Poland), is a mathematician specializing in the fields of knot theory and topology.

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Jones polynomial

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

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Kenneth Millett

Kenneth C. Millett (born 1941) is a professor of mathematics at the University of California, Santa Barbara.

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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.

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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.

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Knot theory

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

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Louis Kauffman

Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, topologist, and professor of Mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago.

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

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Octacube (sculpture)

The Octacube is a large, steel sculpture of a mathematical object: the 24-cell or "octacube".

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Peter J. Freyd

Peter J. Freyd (born February 5, 1936) is an American mathematician, a professor at the University of Pennsylvania, known for work in category theory and for founding the False Memory Syndrome Foundation.

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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.

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Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.

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Quantum invariant

In the mathematical field of knot theory, a quantum knot invariant or quantum invariant of a knot or link is a linear sum of colored Jones polynomial of surgery presentations of the knot complement.

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Skein relation

Skein relations are a mathematical tool used to study knots.

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W. B. R. Lickorish

William Bernard Raymond Lickorish (born 19 February 1938) is a mathematician.

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Redirects here:

FLYPMOTH polynomial, HOMFLY, HOMFLY invariant, HOMFLY(PT) polynomial, HOMFLYPT polynomial, Homfly polynomial, LYMPHTOFU polynomial.


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

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