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On Polynomial Invariants for Knots and Links

Citation

Ho, Chi Fai (1986) On Polynomial Invariants for Knots and Links. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/2tfc-f172. https://resolver.caltech.edu/CaltechTHESIS:04122019-153128474

Abstract

This thesis presents an investigation of many known polynomial invariants of knots and links. Following Alexander's original idea, we define another multi-indeterminant polynomial for links and show that it satisfies some of Torres' conditions. We conjecture that they are equivalent.

Conway polynomials have been known since the sixties. In this paper, we show that the polynomials of various orientations of a link are related, at least in the first and second coefficients. The relationship can be expressed as a function of the Conway polynomials of all sublinks.

A new invariant polynomial of knots and links has been discovered which is independent of the orientation. This polynomial is also invariant of link inverses. Moreover, it is different from the Conway polynomial and the newly discovered HOMFLY polynomial. It distinguishes the trivial 3-unlink and the Borremean ring of 3 components. Various properties of the polynomial are studied.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Fuller, F. Brock
Thesis Committee:
  • Fuller, F. Brock (chair)
  • Anderson, Donald L.
  • Wilson, Richard M.
  • Wales, David B.
Defense Date:18 May 1986
Record Number:CaltechTHESIS:04122019-153128474
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:04122019-153128474
DOI:10.7907/2tfc-f172
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11454
Collection:CaltechTHESIS
Deposited By: Melissa Ray
Deposited On:15 Apr 2019 14:30
Last Modified:16 Apr 2021 23:26

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