Colored Alexander invariants and cone-manifolds
type: Item
instance of: scholarly article
title: Colored Alexander invariants and cone-manifolds
zbMATH Open document ID: 1157.57007
author: Jun Murakami
published in: Osaka Journal of Mathematics
publication date: 2008-08-11T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.ojm/1216151113
review text: The author introduces the ``colored Alexander invariant,'' a framed version of the colored link invariant of \textit{Y. Akutsu, T. Deguchi} and \textit{T. Ohtsuki} [J. Knot Theory Ramifications 1, No.~2, 161--184 (1992; Zbl 0758.57004)]. In analogy with \textit{R. M. Kashaev}'s conjecture [Mod. Phys. Lett. A 10, No.~19, 1409--1418 (1995; Zbl 1022.81574); see also \textit{H. Murakami, J. Kurakami, M. Okamoto, T. Takata} and \textit{Y. Yokota}, Exp. Math. 11, No.~3, 427--435 (2002; Zbl 1117.57300)], the author conjectures that the colored Alexander invariant is related to the volumes of knot and link cone-manifolds. Detailed calculations show that the figure-eight knot, Whitehead's link and the Borromean rings satisfy the conjecture.
reviewed by: L. Traldi
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 20G42
zbMATH DE Number: 5309641
zbMATH Keywords: colored Alexander invariant
zbMATH Keywords: cone manifold
zbMATH Keywords: volume
zbMATH Keywords: \(A\)-polynomial
MaRDI profile type: Publication
cites work: INVARIANTS OF COLORED LINKS
cites work: Q4338898
cites work: On the colored Jones polynomials of some simple links
cites work: A FORMULA FOR THE A-POLYNOMIAL OF TWIST KNOTS
cites work: The hyperbolic volume of knots from the quantum dilogarithm
cites work: On the volume of hyperbolic polyhedra
cites work: Q4462753
cites work: Q4658786
cites work: Kashaev's Conjecture and the Chern-Simons Invariants of Knots and Links
cites work: The colored Jones polynomials of the figure-eight knot and its Dehn surgery spaces
cites work: A state model for the multi-variable Alexander polynomial
cites work: From the Jones Polynomial to the A-Polynomial of Hyperbolic Knots
description: scientific article; zbMATH DE number 5309641