Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function (Q998012)

The author defines a partition function on cusped hyperbolic manifolds with an ideal triangulation using Faddeev's quantum dilogarithm function. Relationships between this partition function and various other quantities (hyperbolic volume of a knot complement, the colored Jones polynomials, the Kashaev invariant, the \(A\)-polynomial, and the Neumann-Zagier potential function) are discussed with numerous examples given in an appendix.