Algorithms for skein manipulation and automation of skein computations

dc.contributor.committeeChairGelca, Razvan
dc.contributor.committeeChairPavlov, Dmitri
dc.contributor.committeeChairHamilton, Alastair
dc.creatorHarris, Rachel
dc.creator.orcid0000-0001-6292-8144
dc.date.accessioned2021-11-09T16:08:34Z
dc.date.available2021-11-09T16:08:34Z
dc.date.created2021-08
dc.date.issued2021-08
dc.date.submittedAugust 2021
dc.date.updated2021-11-09T16:08:35Z
dc.description.abstractSkein manipulations prove to be computationally intensive due to the exponential nature of skein relations. Resolving each crossing in a knot diagram produces 2 new knot diagrams; knot diagrams with over 5 crossings become increasingly difficult to work with. In this work, I introduce a method for automating these computations using algorithms developed to perform computations in the knot complement. This method is developed for all 2-bridge knots, particularly twist knots and (2,2p+1)-torus knots, but can be extended to other families with modification. After showing these algorithms produce the desired result, I demonstrate their implementation in a Python program. This program is used to to compute several known examples, demonstrating how results obtained through several months of work can be can now be obtained in less than 5 minutes. This program will be used for testing various hypotheses in $SU(2)$ Chern-Simons theory.
dc.description.abstractEmbargo status: Restricted to TTU community only. To view, login with your eRaider (top right). Others may request the author grant access exception by clicking on the PDF link to the left.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2346/88237
dc.language.isoeng
dc.rights.availabilityRestricted to TTU community only.
dc.subjectSkein
dc.subjectSkeins
dc.subjectKnot
dc.subjectKnots
dc.subjectTwist
dc.subject2-Bridge
dc.titleAlgorithms for skein manipulation and automation of skein computations
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics and Statistics
thesis.degree.disciplineMathematics
thesis.degree.grantorTexas Tech University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy

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