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dc.contributor.authorTran, Anh Tuanen_US
dc.date.accessioned2012-09-20T18:20:29Z
dc.date.available2012-09-20T18:20:29Z
dc.date.issued2012-06-21en_US
dc.identifier.urihttp://hdl.handle.net/1853/44811
dc.description.abstractThis dissertation studies quantum invariants of knots and links, particularly the colored Jones polynomials, and their relationships with classical invariants like the hyperbolic volume and the A-polynomial. We consider the volume conjecture that relates the Kashaev invariant, a specialization of the colored Jones polynomial at a specific root of unity, and the hyperbolic volume of a link; and the AJ conjecture that relates the colored Jones polynomial and the A-polynomial of a knot. We establish the AJ conjecture for some big classes of two-bridge knots and pretzel knots, and confirm the volume conjecture for some cables of knots.en_US
dc.publisherGeorgia Institute of Technologyen_US
dc.subjectVolume conjectureen_US
dc.subjectAJ conjectureen_US
dc.subjectSkein moduleen_US
dc.subjectColored Jones polynomialen_US
dc.subjectA-polynomialen_US
dc.subject.lcshKnot theory
dc.subject.lcshSymmetry (Mathematics)
dc.subject.lcshInvariants
dc.subject.lcshInvariant manifolds
dc.subject.lcshHyperbolic spaces
dc.titleThe volume conjecture, the aj conjectures and skein modulesen_US
dc.typeDissertationen_US
dc.description.degreePhDen_US
dc.contributor.departmentMathematicsen_US
dc.description.advisorCommittee Chair: Le, Thang; Committee Member: Etnyre, John; Committee Member: Garoufalidis, Stavros; Committee Member: Gilmer, Patrick ; Committee Member: Margalit, Danen_US


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