Title:
The volume conjecture, the aj conjectures and skein modules
The volume conjecture, the aj conjectures and skein modules
Author(s)
Tran, Anh Tuan
Advisor(s)
Le, Thang
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Abstract
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.
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Date Issued
2012-06-21
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Text
Resource Subtype
Dissertation