A bigraded version of the Weil algebra and of the Weil homomorphism for Donaldson invariants

TL;DR

This paper introduces a bigraded generalization of the Weil algebra and its characteristic homomorphism, extending the framework to include Donaldson invariants alongside traditional characteristic classes.

Contribution

It presents a novel bigraded version of the Weil algebra and characteristic homomorphism that incorporates Donaldson invariants, expanding the algebraic tools in differential geometry.

Findings

Bigraded Weil algebra structure established

Characteristic homomorphism extended to Donaldson invariants

Framework unifies characteristic classes and Donaldson invariants

Abstract

We describe a bigraded generalization of the Weil algebra, of its basis and of the characteristic homomorphism which besides ordinary characteristic classes also maps on Donaldson invariants.