A geometric approach to full Colombeau algebras

TL;DR

This paper introduces a geometric framework for constructing diffeomorphism invariant full Colombeau algebras, providing clearer insights into their intrinsic structure on manifolds.

Contribution

It offers a new geometric approach to the construction of full Colombeau algebras that enhances understanding of their intrinsic properties on manifolds.

Findings

Provides a geometric perspective on Colombeau algebras

Clarifies the construction of the algebra $ ilde{ ext{G}}(M)$

Improves understanding of diffeomorphism invariance in Colombeau algebras

Abstract

We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view on the construction of the intrinsically defined algebra $\hat{\mathcal G}(M)$ on the manifold $M$ given in (Grosser et al., Adv. Math. 166 (2002), 179--206).