Optimistic limits of Kashaev invariants and complex volumes of hyperbolic links (Q2930080)

Motivated by the volume conjecture (see [\textit{R. M. Kashaev}, Lett. Math. Phys. 39, No. 3, 269--275 (1997; Zbl 0876.57007)], [\textit{H. Murakami} and \textit{J. Murakami}, Acta Math. 186, No. 1, 85--104 (2001; Zbl 0983.57009)]), Yokota suggested a way to calculate the complex volume (hyperbolic volume + \(\sqrt{-1}\times\) Chern-Simons invariant) for a hyperbolic knot \(K\) in the three-sphere \(S^3\) from a knot diagram [\textit{Y. Yokota}, J. Knot Theory Ramifications 20, No. 7, 955--976 (2011; Zbl 1226.57025)]. In his method one first decomposes the space \(S^3\setminus(K\cup\{\pm\infty\})\) into octahedra, and then deforms it to obtain \(S^3\setminus{K}\), where \(\pm\infty\) are two points in \(S^3\).NEWLINENEWLINEIn the paper under review the authors improve his method to calculate the complex volume directly from \(S^3\setminus(K\cup\{\pm\infty\})\) by using Thurston's spinning construction (see [\textit{W. P. Thurston}, Ann. Math. (2) 124, 203--246 (1986; Zbl 0668.57015)], [\textit{F. Luo} et al., Proc. Am. Math. Soc. 141, No. 1, 335--350 (2013; Zbl 1272.57004)]). Note that their method works more generally than Yokota's, including links. Note also that both Yokota and the authors use \textit{C. K. Zickert}'s formula to calculate the complex volume [Duke Math. J. 150, No. 3, 489--532 (2009; Zbl 1246.58019)].