Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial
The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots...
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1986
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ndltd-unt.edu-info-ark-67531-metadc5010962019-03-12T05:36:53Z Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial Woodard, Mary Kay Conway polynomial invariant of knots knot polynomials Knot theory. Alexander ideals. The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define the Conway polynomial, the Axioms for Computation are given and many examples of their use are included. A major result of this investigation is the proof of topological invariance of these polynomials and the proof that the axioms are sufficient for the calculation of the knot polynomial for any given knot or link. North Texas State University Brand, Neal E. Kung, Joseph P. S. 1986-12 Thesis or Dissertation ii, 76 leaves : ill. Text local-cont-no: 1002775298-Woodard call-no: 379 N81 no.6318 oclc: 16699537 untcat: b1380476 https://digital.library.unt.edu/ark:/67531/metadc501096/ ark: ark:/67531/metadc501096 English Public Woodard, Mary Kay Copyright Copyright is held by the author, unless otherwise noted. All rights reserved. |
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English |
format |
Others
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Conway polynomial invariant of knots knot polynomials Knot theory. Alexander ideals. |
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Conway polynomial invariant of knots knot polynomials Knot theory. Alexander ideals. Woodard, Mary Kay Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
description |
The problem under consideration is that of determining a simple and effective invariant of knots. To this end, the Conway polynomial is defined as a generalization of Alexander's original knot polynomial. It is noted, however, that the Conway polynomial is not a complete invariant. If two knots are equivalent, as defined in this investigation, then they receive identical polynomials. Yet, if two knots have identical polynomials, no information about their equivalence may be obtained. To define the Conway polynomial, the Axioms for Computation are given and many examples of their use are included. A major result of this investigation is the proof of topological invariance of these polynomials and the proof that the axioms are sufficient for the calculation of the knot polynomial for any given knot or link. |
author2 |
Brand, Neal E. |
author_facet |
Brand, Neal E. Woodard, Mary Kay |
author |
Woodard, Mary Kay |
author_sort |
Woodard, Mary Kay |
title |
Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
title_short |
Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
title_full |
Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
title_fullStr |
Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
title_full_unstemmed |
Conway's Link Polynomial: a Generalization of the Classic Alexander's Knot Polynomial |
title_sort |
conway's link polynomial: a generalization of the classic alexander's knot polynomial |
publisher |
North Texas State University |
publishDate |
1986 |
url |
https://digital.library.unt.edu/ark:/67531/metadc501096/ |
work_keys_str_mv |
AT woodardmarykay conwayslinkpolynomialageneralizationoftheclassicalexandersknotpolynomial |
_version_ |
1719001630498619392 |