Finite Nocommutative Coverings and Flat Connections

TL;DR

This paper explores the noncommutative analog of the classical correspondence between flat connections and fundamental group representations, extending the concept to finite nocommutative coverings.

Contribution

It introduces a noncommutative framework for understanding flat connections via finite nocommutative coverings, generalizing classical results.

Findings

Established a noncommutative analog of the fundamental group correspondence.

Characterized flat connections in the context of nocommutative coverings.

Extended classical geometric concepts to noncommutative geometry.

Abstract

Any flat connection on a principal fibre bundle comes from a linear representation of the fundamental group. The noncommutative analog of this fact is discussed here.