Path-component invariants for spaces of positive scalar curvature metrics

TL;DR

This paper develops a new invariant for the space of positive scalar curvature metrics on certain product manifolds, extending the Kreck-Stolz s-invariant to cases where it was previously undefined.

Contribution

It introduces an analogous invariant for product manifolds, broadening the applicability of invariants in positive scalar curvature geometry.

Findings

Constructed a new invariant for specific product manifolds.

Extended the scope of path-component invariants beyond previous limitations.

Provided tools for distinguishing positive scalar curvature metrics in new settings.

Abstract

The Kreck-Stolz $s$-invariant is a classic path-component invariant for the space and moduli space of positive scalar curvature metrics. It is an absolute (as opposed to relative) invariant, but this strength comes at the expense of being defined only under restrictive topological conditions. The aim of this paper is to construct an analogous invariant for certain product manifolds on which the $s$-invariant is not defined.