Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function
type: Item
instance of: scholarly article
title: Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function
zbMATH Open document ID: 1139.57013
author: Kazuhiro Hikami
published in: Journal of Geometry and Physics
publication date: 2007-08-10T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0604094
review text: 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.
reviewed by: Sam Nelson
Mathematics Subject Classification ID: 57M27
zbMATH DE Number: 5178550
zbMATH Keywords: quantum invariant
zbMATH Keywords: Cherns-Simons theory
zbMATH Keywords: colored Jones polynomial
zbMATH Keywords: hyperbolic manifolds
zbMATH Keywords: \(A\)-polynomial
zbMATH Keywords: Neumann-Zagier function
zbMATH Keywords: quantum dilogarithm function
describes a project that uses: KnotPlot
describes a project that uses: SnapPea
describes a project that uses: Knotscape
MaRDI profile type: Publication
OpenAlex ID: W1479665659
Wikidata QID: Q123000794
arXiv ID: math/0604094
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Generalized volume conjecture and the \(A\)-polynomials: The Neumann-Zagier potential function as a classical limit of the partition function (DOI)
DOI: 10.1016/J.GEOMPHYS.2007.03.008

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