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.

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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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Alexander Polynomial -- from Wolfram MathWorld
Alexander polynomial. DOWNLOAD Mathematica Notebook. The Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander ...
mathworld.wolfram.com/AlexanderPolynomial.html
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The Alexander Polynomial
The Alexander polynomial. The woefully overlooked granddaddy of knot polynomials. Julia Collins. May 25, 2007. Abstract. Once upon a time (actually in 1928) ...
www.maths.ed.ac.uk/~s0681349/GeomClub.pdf
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ALEXANDER POLYNOMIAL OF KNOTS 1 ... - Mathematics
May 26, 2004 ... Alexander polynomial OF KNOTS. TERM PAPER FOR MATH 215B, SPRING 2004. JOSEPHINE YU. Abstract. The Alexander polynomial ...
math.berkeley.edu/~hutching/teach/215b-2004/yu.pdf
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Alexander-Conway and Jones Polynomials
CS E6204 Lectures 9b and 10. Alexander-Conway and Jones Polynomials. ∗. Abstract. Before the 1920's, there were a few scattered papers concerning knots ...
www.cs.columbia.edu/~cs6204/files/Lec9b,10.pdf
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A SHORT INTRODUCTION TO THE ALEXANDER POLYNOMIAL ...
A SHORT INTRODUCTION TO. THE Alexander polynomial. GWÉNAËL MASSUYEAU. Abstract. These informal notes accompany a talk given in Grenoble ...
www-irma.u-strasbg.fr/~massuyea/talks/Alex.pdf
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The Alexander-Conway Polynomial - Knot Atlas
In[2]:= ?Alexander. Alexander[K][t] computes the Alexander polynomial of a knot K as a function of the variable t. Alexander[K, r][t] computes a basis of the r'th ...
katlas.org/wiki/The_Alexander-Conway_Polynomial
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The Alexander polynomial, coloring, and ... - it-educ.jmu.edu
THE Alexander polynomial, COLORING, AND. DETERMINANTS OF KNOTS. RAQUEL LOPEZ. Abstract. We give an algorithm to calculate the Alexander ...
educ.jmu.edu/~taalmala/OJUPKT/lopez.pdf
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Alexander Polynomials of Two-Bridge Knots and Links
Alexander polynomials of Two-Bridge Knots and Links. Rob Gaebler. Jim Hoste, Advisor. Weiquing Gu, Reader. May, 2004. Department of Mathematics ...
www.math.hmc.edu/seniorthesis/archives/2004/rgaebler/rgaebler-2004-thesis.pdf
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The Alexander Polynomial For Knots
The Alexander polynomial For Knots. Sonia Todorova. May 29, 2007. Thesis adviser: Veronique Godin. A thesis submitted to the. Department of Mathematics at ...
Search results for "Alexander polynomial"
Alexander polynomial in science
Lecture Series in Topology: The Twisted Alexander Polynomial ...
The Twisted Alexander polynomial. Ten lectures by Dan Silver (University of South Alabama) and Su...
GEOMETRY, ALGEBRA, AND THE ALEXANDER POLYNOMIAL
Knot Theory, a lively exposition of the mathematics of knotting, will appeal to a diverse audience from the undergraduate seeking experience outside the ...
[PDF]Alexander and Conway polynomials of Torus knots - Trace - The ...
Alexander and Conway polynomials of Torus knots. Katherine Ellen Louise Agle. University of Tennessee - Knoxville, kagle@utk.edu. This Thesis is brought to ...
Twisted Alexander polynomials of 2-bridge knots
Jun 9, 2012 ... Jim Hoste (Pitzer College), Patrick D. Shanahan (Loyola Marymount University). We investigate the twisted Alexander polynomial of a 2-bridge ...
[PDF]three routes to the Alexander Polynomial - UCL
May 14, 2005 ... Topological invariants of knots: three routes to the. Alexander polynomial. Edward Long. Manchester University. MT4000 Double Project.
Knots, graphs, and the Alexander polynomial | Mathematical Institute ...
Feb 25, 2010 ... In 2008, Juhasz published the following result, which was proved using sutured Floer homology. Let \$ K \$ be a prime, alternating knot. Let \$ a \$ ...
The Multivariable Alexander Polynomial on Tangles
Feb 15, 2011 ... T-Space at The University of Toronto Libraries > ... Abstract: The multivariable Alexander polynomial (MVA) is a classical invariant of knots and ...
an investigation of alexander polynomials - DRUM - University of ...
Title: AN INVESTIGATION OF Alexander polynomialS. Authors: Horvath, Justina E. Advisors: Washington, Lawrence C. Department/Program ...
A Remark on the Alexander Polynomial Criterion for the Bi ...
Jan 12, 2012 ... Graduate School of Mathematical Science, University of Tokyo, 3-8-1 ... which uses the classical Alexander polynomial, is not strengthened ...
[PDF]Zeros of the Jones polynomial - University of California, Riverside
Oliver Dasbach (Louisiana State University). Zhixiong Tao ... is the Alexander polynomial of a certain knot iff ... polynomial with integer coefficients is the Jones.
Books on the term Alexander polynomial
CRC Concise Encyclopedia of Mathematics, Second Edition
Eric W. Weisstein, 2010
1976). Because the ALEXANDER INVARIANT of a TAME KNOT in S3 has a SQUARE presentation MATRIX, its ALEXANDER IDEAL is PRINCIPAL and it has an Alexander polynomial denoted &(t). Let 4* be the MATRDC PRODUCT of BRAID ...
Solving Polynomial Systems Using Continuation for Engineering and ...
Alexander Morgan, 2009
This book introduces the numerical technique of polynomial continuation, which is used to compute solutions to systems of polynomial equations.
Peter R. Cromwell, 2004
In this chapter we shall introduce polynomial- valued invariants. First we shall derive the classical Alexander polynomial from the Seifcrt matrix. The Conway polynomial has an axiomatic definition based on relationships between diagrams .
Knots and Physics
Louis H. Kauffman, 2013
The Alexander polynomial. The main purpose of this section is to show that a Yang-Baxter model essentially similar to the one discussed in section 11° can produce the AlexanderConway polynomial. Along with this construction a number of ...
The Knot Book: An Elementary Introduction to the Mathematical ...
Although we do not prove it here, these two rules are enough to ensure that the Alexander polynomial is an invariant for ... In particular, this means that if we are given a projection of a knot, we can compute the Alexander polynomial of the knot ...
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Blog posts on the term
Alexander polynomial
The Alexander polynomial as quantum invariant of links - INSPIRE-HEP
In these notes we collect some results about finite dimensional representations of Uq(gl(1|1)) and related invariants of framed tangles which are well-known to experts but difficult to find in the literature. In particular, we give an explicit description of the ribbon structure on the category of finite dimensional Uq(gl(1|1))-representation and we use it to construct the corresponding quantum invariant of framed tangles. We explain in detail why this invariant vanishes on closed links and how one can modify the construction to get a nonzero invariant of framed closed links. Finally we show how to obtain the Alexander polynomial by considering the vector representation of Uq(gl(1|1)). Sartori, Antonio
inspirehep.net/record/1247324
The Alexander Polynomial as a Quantum Invariant: Part 3 | Low Dimensional Topology
My original intention for this post was to summarize Chapter 2.3 and Appendix C of Quantum Invariants by Tomotada Ohtsuki, with some commentary. But it looks like an opaque calculation to me at the moment- calculate the R-matrix of the Alexander polynomial from its Skein relation, and lo-and-behold it coincides with the R-matrix you get…
ldtopology.wordpress.com/2010/03/04/the-alexander-polynomial-as-a-quantum-invariant-part-3/
Twisted Alexander polynomials of hyperbolic knots | driven to abstraction
I've recently been helping Stefan Friedl and Nathan Dunfield with an interesting project looking at the twisted Alexander polynomials of hyperbolic knots, which has now resulted in two papers [2,3], some software [1], and a number of unanswered questions. I've found it all fascinating and have learned a lot of interesting stuff about mathematics (twisted…
dtoa.wordpress.com/2011/08/18/twisted-alexander-polynomials-of-hyperbolic-knots/
Trees, The BEST Theorem, and Alexander Polynomials | Concrete Nonsense
Most of my "free math time" has been used to study for quals, but today I've made myself post to stop Steven from taking over this blog. One of my favorite elementary algebric combinatorial results is the Matrix Tree Theorem, which states: In a nondirected graph with vertices labelled \$latex 1, 2, \ldots n\$, the…
concretenonsense.wordpress.com/2009/08/20/trees-the-best-theorem-and-alexander-polynomials/
"Alexander and Conway polynomials of Torus knots" by Katherine Ellen Louise Agle
We disprove the conjecture that if K is amphicheiral and K is concordant to K', then CK'(z)CK'(iz)CK\(z2) is a perfect square inside the ring of power series with integer coefficients. The Alexander polynomial of (p,q)-torus knots are found to be of the form AT(p,q)(t)= (f(tq))/(f(t)) where f(t)=1+t+t2+...+tp-1. Also, for (pn,q)-torus knots, the Alexander polynomial factors into the form AT(pn ,q)=f(t)f(tp)f(tp2 )...f(tpn-2 )f(tpn-1 ). A new conversion from the Alexander polynomial to the Conway polynomial is discussed using the Lucas polynomial. This result is used to show that the Conway polynomial of (2n,q)-torus knots are of the form CT(2n ,q)(z)=K1K2...Kn where K1=Fq(z), Fq(z) being the Fibonacci polynomial, and Ki(z)=Ki-1(√z4+4z2).