Non-negative versus positive scalar curvature

TL;DR

This paper demonstrates that many results concerning positive scalar curvature metrics, established via index theory, can be extended to include non-negative scalar curvature metrics, with explicit generalizations provided.

Contribution

It introduces a method to extend classical results from positive to non-negative scalar curvature metrics using index theory.

Findings

Classical results on positive scalar curvature moduli spaces are generalized to non-negative scalar curvature.

Explicit examples of these generalizations are provided.

The approach broadens the applicability of index theory in scalar curvature geometry.

Abstract

We show that results about spaces or moduli spaces of positive scalar curvature metrics proved using index theory can typically be extended to non-negative scalar curvature metrics. We illustrate this by providing explicit generalizations of some classical results concerning moduli spaces of positive scalar curvature metrics.