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.
| Identifer | oai:union.ndltd.org:GATECH/oai:smartech.gatech.edu:1853/44811 |
| Date | 21 June 2012 |
| Creators | Tran, Anh Tuan |
| Publisher | Georgia Institute of Technology |
| Source Sets | Georgia Tech Electronic Thesis and Dissertation Archive |
| Detected Language | English |
| Type | Dissertation |
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