Jets and connections in commutative and noncommutative geometry

TL;DR

This paper explores the differences in defining connections on modules within commutative versus noncommutative geometry, highlighting the complexities and distinctions in noncommutative settings.

Contribution

It clarifies that equivalent definitions of connections in commutative geometry do not carry over straightforwardly to noncommutative geometry, emphasizing the need for different approaches.

Findings

Connections definitions differ significantly between commutative and noncommutative cases.

Noncommutative geometry requires distinct frameworks for connections.

The paper highlights the non-equivalence of connection definitions in noncommutative modules.

Abstract

It is emphasized that equivalent definitions of connections on modules over commutative rings are not so in noncommutative geometry.