Local index theory and the Riemann-Roch-Grothendieck theorem for complex flat vector bundles II

TL;DR

This paper proves a version of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles, focusing on the real part at the differential form level, advancing understanding in differential geometry.

Contribution

It establishes the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level, extending previous theoretical frameworks.

Findings

Proof of the real part of the theorem at the differential form level

Advancement in the understanding of complex flat vector bundles

Extension of classical index theory results

Abstract

In this paper, we prove the real part of the Riemann-Roch-Grothendieck theorem for complex flat vector bundles at the differential form level.