The Chern class for $K_3$ and the cyclic quantum dilogarithm

Abstract

In this note we confirm the conjecture of Calegari, Garoufalidis and Zagier in their recent paper in Ann. Sci. École Normale Sup. that $R_{\zeta }=c_{\zeta }^2$, where $R_{\zeta }$ is their map on $K_3$ defined using the cyclic quantum dilogarithm and $c_{\zeta }$ is the Chern class map on $K_3$.

8 pages. Extensively rewritten for greater clarity of the main argument Now revised in line with referee comments. To appear in Journal of Algebra