Multitransgression and regulators

TL;DR

This paper introduces a simplicial formalism for higher order characteristic classes related to the Chern character, simplifying computations and enabling new comparisons and explicit formulas for regulators and polylogarithms.

Contribution

It generalizes secondary characteristic classes and provides a simpler computational framework for regulators and polylogarithms.

Findings

Comparison of Borel and Beilinson regulators

Explicit formula for the real single-valued function of Grassmannian polylogarithm

Simplified computation of higher order characteristic classes

Abstract

In a parallel way to the work of Wang, we define higher order characteristic classes associated with the Chern character, generalizing the work of Bott-Chern and Gillet-Soul\'e on secondary characteristic classes. Our formalism is simplicial and the computations are easier. As a consequence, we obtain the comparison of Borel and Beilinson regulators and an explicit formula for the real single-valued function associated with the Grasmannian polylogarithm.