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

TL;DR

This paper establishes $10/8$-type inequalities for certain end-periodic 4-manifolds with positive scalar curvature on the ends and uses these results to identify new closed 4-manifolds that cannot support positive scalar curvature metrics.

Contribution

It introduces $10/8$-type inequalities for end-periodic 4-manifolds with positive scalar curvature on the ends and constructs new examples of 4-manifolds without positive scalar curvature.

Findings

Proved $10/8$-type inequalities for end-periodic 4-manifolds

Constructed new closed 4-manifolds without positive scalar curvature

Extended scalar curvature obstructions to end-periodic settings

Abstract

We show $ 10/8$-type inequalities for some end-periodic $4$-manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed $4$-manifolds which do not admit positive scalar curvature metrics.