An open four-manifold having no instanton

TL;DR

This paper constructs a non-compact four-manifold that does not admit any non-flat instantons, contrasting with Taubes' result for compact manifolds.

Contribution

It demonstrates the existence of a non-compact four-manifold with no non-flat instantons, providing a counterexample to the extension of Taubes' theorem.

Findings

Existence of a non-compact four-manifold with no non-flat instantons

Contrasts with Taubes' theorem for compact manifolds

Provides new insights into instanton theory on non-compact manifolds

Abstract

Taubes proved that all compact oriented four-manifolds admit non-flat instantons. We show that there exists a non-compact oriented four-manifold having no non-flat instanton.