Polynomial knot invariant
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.

This is an excerpt from the article Polynomial knot invariant from the Wikipedia free encyclopedia. A list of authors is available at Wikipedia.
The article Polynomial knot invariant at en.wikipedia.org was accessed 11 times in the last 30 days. (as of: 12/22/2013)
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Knot polynomial - Wikipedia, the free encyclopedia
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 ...
en.wikipedia.org/wiki/Knot_polynomial
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Jones polynomial - Wikipedia, the free encyclopedia
In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an ...
en.wikipedia.org/wiki/Jones_polynomial
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Alexander polynomial - Wikipedia, the free encyclopedia
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II ...
en.wikipedia.org/wiki/Alexander_polynomial
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Knot invariant - Wikipedia, the free encyclopedia
Other examples are knot polynomials, such as the Jones polynomial, which are currently among the most useful invariants for distinguishing knots from one ...
en.wikipedia.org/wiki/Knot_invariant
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Topological invariants of knots: three routes to the Alexander ... - UCL
May 14, 2005 ... logical invariants of knots and links, in which the author introduces the Alexander polynomial. While doing background reading on the subject, ...
www.ucl.ac.uk/~ucbpeal/alexandermac.pdf
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Polynomial Invariants of Knots - Albany Consort
Polynomial. Invariants of Knots. Why would we need a polynomial to identify a knot? Well, if we were to use simply a number, such as the bridge number ...
www.albanyconsort.com/polyinv/polyinv.pdf
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Knot Invariant -- from Wolfram MathWorld
Standard knot invariants include the fundamental group of the knot complement, numerical knot invariants (such as Vassiliev invariants), polynomial invariants ...
mathworld.wolfram.com/KnotInvariant.html
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Alexander Polynomial -- from Wolfram MathWorld
The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot ...
mathworld.wolfram.com/AlexanderPolynomial.html
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Knot Theory Invariants: The HOMFLY Polynomial - Library
A brief article on the HOMFLY polynomial and how it is calculated.
library.thinkquest.org/12295/data/Invariants/Articles/HOMFLY.html
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Knot Theory Invariants: The Jones Polynomial - Library
The Jones Polynomial. Historical Background. The Jones Polynomial was discovered by Vaughan F. R. Jones in 1984. Unlike the Alexander Polynomial, the ...
library.thinkquest.org/12295/data/Invariants/Articles/Jones.html
Search results for "Polynomial knot invariant"
Polynomial knot invariant in science
KnotInfo - Indiana University
Aug 25, 2012 ... Table of Knot Invariants. Please try LinkInfo:Table of Link Invariants and give us feedback. ... Show polynomials as coefficient vectors ...
Knot polynomials and Vassiliev's invariants - Springer
Since Vassiliev's knot invariants have a firm grounding in classical topology, one ... a first step in understanding the Jones polynomial by topological methods. ... 1. Department of Mathematics, Columbia University, 10027, New York, NY, USA ...
Knot theory - Wikipedia, the free encyclopedia
Important invariants include knot polynomials, knot groups, and hyperbolic ..... Sossinsky, Alexei (2002), Knots, mathematics with a twist, Harvard University ...
[PDF]The New Polynomial Invariants of Knots and Links - University of ...
Jun 26, 2007 ... The New Polynomial Invariants of Knots and Links. W. B. R. Lickorish; K. C. Millett . Mathematics Magazine, Vol. 61, No. 1. (Feb., 1988), pp. 3-23 ...
Columbia Geometric Topology Seminar - Columbia University
Noah Snyder, Columbia University, “Knot polynomial identities and coincidences of small quantum groups”. I'll introduce skein theoretic knot invariants coming ...
Vassiliev Invariant -- from Wolfram MathWorld
The notion of finite type (a.k.a. Vassiliev) knot invariants was independently invented by ... Vassiliev invariants are at least as strong as all known polynomial knot ... Lectures delivered at Graduate School of Mathematical Sciences, University of ...
[PDF]VASSILIEV INVARIANTS AS POLYNOMIALS
VASSILIEV INVARIANTS AS POLYNOMIALS. SIMON WILLERTON. Department of Mathematics and Statistics, University of Edinburgh. James Clerk Maxwell ...
Dror Bar-Natan: Publications
We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of the computationally ...
Quantum Curves and Quantum Knot Invariants - Banff International ...
Motohico Mulase (University of California, Davis) ... Compared to these, the A-polynomials of knots are “classical” invariants, in the sense of classical mechanics ...
Books on the term Polynomial knot invariant
Bifurcations and Periodic Orbits of Vector Fields
Dana Schlomiuk, 1993
Appendix: Polynomial. invariants. The knot and link invariants used in this paper have all been numerical invariants, that is, ... Analogously, a great deal of attention of late has centered around polynomial knot and link invariants, which we ...
Beginning topology
Sue Goodman, 2005
Braid groups are particularly useful in applications of knot theory to statistical mechanics and played an instrumental role in Jones's discovery of an important Polynomial knot invariant. (We take a look at knot polynomials in the next section. ) ...
Braid Group, Knot Theory, and Statistical Mechanics II
Chen Ning Yang, Mo-Lin Ge, 1994
_5_£, 365- 378(1983). 47) Hennings, M.A., "A polynomial invariant for banded links" (preprint 1988). 48) Hitt, L.R., and Silver, D.S., "Stalling's twists and the Jones polynomial" (to appear). 49) Ho, C.F., "A new polynomial invariant for knots and ...
Loops, Knots, Gauge Theories and Quantum Gravity
Rodolfo Gambini, Jorge Pullin, 2000
10.3.2 Skein relations, ambient and regular isotopies A knot (or link) polynomial is an assignment of a finite set of numbers to a knot (or link) that is invariant under ambient or regular isotopies. Given a knot 7 one gets a polynomial* P(J)q in an ...
Notions of positivity and the geometry of polynomials
Petter Brèandâen, Mikael Passare, Mihai Putinar, 2011
We describe the algebra of finite-order invariants on the set of all ( ,2)-torus knots. Mathematics Subject Classification (2000). 57M27. Keywords. Finite type invariants, torus knots, polynomials. This paper is an extended exposition of the talk ...

Blog posts on the term
Polynomial knot invariant
Knot polynomial identities and quantum group coincidences (February) | Secret Blogging Seminar
Representation theory, geometry and whatever else we decide is worth writing about today.
sbseminar.wordpress.com/2010/03/01/knot-polynomial-identities-and-quantum-group-coincidences-february/
Multiplication by Infinity: Knot Theory (and the Jones Polynomial)
It is shown that 2+1 dimensional quantum Yang-Mills theory, with an action consisting purely of the Chern-Simons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms. In this version, the Jones polynomial can be generalized fromS 3 to arbitrary three manifolds, giving invariants of three manifolds that are computable from a surgery presentation.
tetrahedral.blogspot.com/2011/03/knot-theory.html
TGD diary: Witten's talk about knot invariants
Lubos gave a link to a recent talk of Witten about knots and quantum physics. While listening the lecture one senses the enormous respect and -I dare say- love that the audience feels towards this silently talking genius completely free of all what might be called ego.