Gauss-Bonnet-Chern theorem and differential characters

TL;DR

This paper extends the Gauss-Bonnet-Chern theorem to differential characters by showing they can be represented via differential forms with singularities, providing a new perspective on classical geometric invariants.

Contribution

It introduces a novel representation of differential characters using singular differential forms and generalizes the Gauss-Bonnet-Chern theorem to this framework.

Findings

Differential characters can be represented by differential forms with singularities.

The Gauss-Bonnet-Chern theorem is lifted to the setting of differential characters.

Provides a new geometric interpretation of classical topological invariants.

Abstract

In this paper we first prove that every differential character can be represented by differential form with singularities. Then we lift the Gauss-Bonnet-Chern theorem for vector bundles to differential characters.