Colored Alexander invariants and cone-manifolds
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.
scientific article; zbMATH DE number 5309641