Moduli spaces of flat Lie algebroid connections

TL;DR

This paper demonstrates that the moduli space of flat irreducible Lie algebroid connections on a compact manifold can be given a natural smooth structure, generalizing known results from complex geometry.

Contribution

It extends the theory of moduli spaces to include flat irreducible Lie algebroid connections, providing a new geometric framework.

Findings

Moduli space has a natural smooth differentiable structure

Generalizes results from complex vector bundle theory

Applicable to flat irreducible Lie algebroid connections

Abstract

We shall prove that a moduli space of flat irreducible Lie algebroid connections over a compact manifold has locally a natural structure of a smooth differentiable space. This is a generalization of some well known results for the moduli space of holomorphic structures on a complex vector bundle over a compact complex manifold.