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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 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.

Identiferoai:union.ndltd.org:unt.edu/info:ark/67531/metadc501096
Date12 1900
CreatorsWoodard, Mary Kay
ContributorsBrand, Neal E., Kung, Joseph P. S.
PublisherNorth Texas State University
Source SetsUniversity of North Texas
LanguageEnglish
Detected LanguageEnglish
TypeThesis or Dissertation
Formatii, 76 leaves : ill., Text
RightsPublic, Woodard, Mary Kay, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved.

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