Positive scalar curvature and 10/8-type inequalities on 4-manifolds with periodic ends (Q2208432)

The authors give a relation between two different types of topics linked via the Seiberg-Witten equations on some 4-manifold with periodic ends. The first topic is the existence of a metric with positive scalar curvature (PSC) on a given manifold. This is a classical object of interest in Riemannian geometry. The second is the \(10/8\)-inequality, regarded as one of the central topics in 4-dimensional topology. The relation exhibited in this paper between these two topics also yields a concrete application, that is, the construction of a new family of closed 4-manifolds which do not admit positive scalar curvature metrics.