Remark on the Serre-Swan theorem for non-compact manifolds

TL;DR

This paper discusses extending the Serre-Swan theorem, which links projective modules and vector bundles, from compact to non-compact manifolds, highlighting its significance in non-commutative geometry.

Contribution

It provides insights into how the Serre-Swan theorem can be generalized to non-compact manifolds, expanding its applicability.

Findings

Extension of the Serre-Swan theorem to non-compact manifolds

Implications for non-commutative geometry

Potential new frameworks for vector bundles on non-compact spaces

Abstract

The Serre-Swan theorem provides the link between projective modules of finite rank and vector bundles over compact manifolds, and plays a prominent role in non-commutative geometry. Its extension to non-compact manifolds is discussed.