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dc.contributor.advisorKauffman, Louis H
dc.creatorSimpson, David H.
dc.date.accessioned2019-08-06T14:17:47Z
dc.date.available2019-08-06T14:17:47Z
dc.date.created2019-05
dc.date.issued2019-02-14
dc.date.submittedMay 2019
dc.identifier.urihttp://hdl.handle.net/10027/23681
dc.description.abstractWe examine the relation between Ribbon Hopf Algebras and 1-1 Tangles -- knot diagrams that are cut at a point with the ends pulled apart. Specifically, we investigate the behavior of one such algebra, introduced in the 1992 paper "On Kauffman’s knot invariants arising from finite-dimensional Hopf algebras" by David Radford. We compile the first-ever results for knots of 3-10 crossings using one of these algebras, and discuss the magnitude of calculations involved, and practical methods of attaining results in reasonable time.
dc.format.mimetypeapplication/pdf
dc.subjectKnot Invariants
dc.subjectHopf Algebras
dc.titleThe Application of Ribbon Hopf Algebras to Invariants of 1-1 Tangles
dc.typeThesis
thesis.degree.departmentMathematics, Statistics and Computer Science
thesis.degree.grantorUniversity of Illinois at Chicago
thesis.degree.levelDoctoral
thesis.degree.namePhD, Doctor of Philosophy
dc.contributor.committeeMemberRadford, David
dc.contributor.committeeMemberShalen, Peter
dc.contributor.committeeMemberTakloo-Bighash, Ramin
dc.contributor.committeeMemberLicht, Arthur
dc.type.materialtext
dc.contributor.chairKauffman, Louis H


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