Positive scalar curvature and homology cobordism invariants

Abstract

We give an obstruction to positive scalar curvature metrics on 4-manifolds with the homology 𝑆 1 × 𝑆 3 described in terms of homology cobordism invariants from Seiberg-Witten theory. The main tool of the proof is a relative Bauer-Furuta-type invariant on a periodic-end 4-manifold.