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The volume conjecture, the aj conjectures and skein modules

This 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.

Identiferoai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/44811
Date21 June 2012
CreatorsTran, Anh Tuan
PublisherGeorgia Institute of Technology
Source SetsGeorgia Tech Electronic Thesis and Dissertation Archive
Detected LanguageEnglish
TypeDissertation

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