Proof of the Strong AJ Conjecture for the Figure 8 Knot

dc.contributor.advisorTran, Anh T.
dc.creatorNguyen, Hoang-An A.
dc.date.accessioned2019-10-08T15:09:03Z
dc.date.available2019-10-08T15:09:03Z
dc.date.created2019-05
dc.date.issued2019-05
dc.date.submittedMay 2019
dc.date.updated2019-10-08T15:09:04Z
dc.description.abstractThe AJ conjecture, formulated by Garoufalidis [7], relates the A-polynomial of a knot and the colored Jones polynomial of a knot. The strong AJ conjecture first proposed in [6] and then modified by Sikora [14], relates the orthogonal ideal to the classical peripheral ideal. The orthogonal ideal is an ideal of the skein module of the torus and the classical peripheral ideal is an ideal of the coordinate ring of the SL(2, C) character variety. This conjecture could be seen as the topological and algebraic structure that underlies the AJ conjecture. The strong AJ conjecture has been confirmed for all torus knots and cables over torus knots. As such, the conjecture has only been confirmed for cases of non-hyperbolic knots. It should be noted that most knots fall into the class of being hyperbolic. In this thesis we confirm the strong AJ conjecture for the figure 8 knot which is the simplest hyperbolic knot.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/10735.1/6973
dc.language.isoen
dc.rights©2019 Hoang-An A. Nguyen
dc.subjectQuantum theory
dc.subjectTopology
dc.subjectModules (Algebra)
dc.subjectKnot polynomials
dc.subjectTorus (Geometry)
dc.subjectGeometry, Hyperbolic
dc.titleProof of the Strong AJ Conjecture for the Figure 8 Knot
dc.typeThesis
dc.type.materialtext
thesis.degree.departmentMathematics
thesis.degree.grantorThe University of Texas at Dallas
thesis.degree.levelMasters
thesis.degree.nameMS

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