Decomposing 4-manifolds with positive scalar curvature

TL;DR

This paper demonstrates a method to decompose any closed, oriented 4-manifold with positive scalar curvature into simpler components using surgeries, connecting it to orbifolds with controlled topological invariants.

Contribution

It introduces a novel decomposition technique for PSC 4-manifolds via surgeries, linking them to orbifolds with specific Betti number constraints.

Findings

Any closed, oriented PSC 4-manifold can be obtained from a PSC 4-orbifold through surgeries.

The resulting orbifold has vanishing first Betti number.

The second Betti number of the orbifold is at most that of the original manifold.

Abstract

We show that every closed, oriented, topologically PSC 4-manifold can be obtained via 0 and 1-surgeries from a topologically PSC 4-orbifold with vanishing first Betti number and second Betti number at most as large as the original one.