Volume conjecture and WKB asymptotics
type: Item
instance of: scholarly article
title: Volume conjecture and WKB asymptotics
zbMATH Open document ID: 1505.57002
DOI: 10.1134/S1995080222110051
published in: Lobachevskii Journal of Mathematics
publication date: 2022-12-05T00:00:00Z
review text: In the paper under review the authors consider the colored Jones polynomials and the \(q\)-difference equations, which are satisfied by it. They investigate the WKB asymptotic behavior of the \(n\)-th Jones polynomial at the roots of unity of the form exp\((2\pi i/N)\), as both \(n\) and \(N\) go to infinity, while \(n/N\) is in the unit interval. The authors then state a theorem on the asymptotic expansion of the general solutions of the \(q\)-difference equations. Based on heuristic and numeric considerations on the colored Jones polynomial, they present a conjecture that is shown to be in accordance with the volume conjecture, for special classes of knots.
reviewed by: Valeriano Aiello
Mathematics Subject Classification ID: 57K10
Mathematics Subject Classification ID: 57K16
zbMATH DE Number: 7626316
zbMATH Keywords: knots
zbMATH Keywords: colored Jones polynomial
zbMATH Keywords: volume conjecture
zbMATH Keywords: WKB asymptotics of solutions to \(q\)-recurrence equation
author: A. I. Aptekarev
author: Tat'yana V. Dudnikova
author: D. N. Tulyakov
MaRDI profile type: Publication
Wikidata QID: Q123309826
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description: scientific article; zbMATH DE number 7626316