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

TL;DR

This paper proves a conjecture relating the cyclic quantum dilogarithm map and the Chern class map on K_3, establishing a precise algebraic relationship between these two constructions.

Contribution

It confirms a conjecture connecting the cyclic quantum dilogarithm and the Chern class on K_3, advancing understanding in algebraic K-theory and quantum invariants.

Findings

Confirmed the conjecture R_ζ = c_ζ^2 on K_3.

Established a fundamental relationship between quantum dilogarithm and Chern class.

Contributed to the theory of algebraic K-theory and quantum invariants.

Abstract

In this note we confirm the conjecture of Calegari, Garoufalidis and Zagier in their recent paper in Ann. Sci. \'{E}cole 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 $K_3$.