A dilogarithmic formula for the Cheeger-Chern-Simons class

TL;DR

This paper introduces a simplified algebraic formula for the Cheeger-Chern-Simons class, making it easier to compute directly on homology classes, advancing the understanding of secondary characteristic classes.

Contribution

It provides a new algebraic and more accessible formula for the Cheeger-Chern-Simons class, improving computational methods.

Findings

Simplified Neumann's formula algebraically

Applicable directly on homology classes in the bar complex

Enhances computational approaches for secondary characteristic classes

Abstract

We present a simplification of Neumann's formula for the universal Cheeger-Chern-Simons class of the second Chern polynomial. Our approach is completely algebraic, and the final formula can be applied directly on a homology class in the bar complex.