Non-commutative coverings spaces

TL;DR

This paper introduces a framework for non-commutative covering spaces using Hopf-Galois theory, exploring their properties and providing examples including non-commutative tori.

Contribution

It defines non-commutative covering spaces and analyzes their properties, extending classical concepts to non-commutative geometry.

Findings

Basic properties of coverings extend to non-commutative cases

Examples include coverings of commutative spaces and non-commutative tori

Framework connects Hopf-Galois theory with non-commutative topology

Abstract

In this article, we will define non-commutative covering spaces using Hopf-Galois theory. We will look at basic properties of covering spaces that still hold for these non-commutative analogues. We will describe examples including coverings of commutative spaces and coverings of non-commutative tori.