On the moduli spaces of metrics with nonnegative sectional curvature

TL;DR

This paper uses the Kreck-Stolz s invariant to analyze the structure of the moduli space of nonnegative sectional curvature metrics, revealing infinitely many disconnected components on specific 7-manifolds, including some with positive curvature.

Contribution

It extends the application of the Kreck-Stolz s invariant to nonnegative sectional curvature metrics, identifying infinitely many components on certain 7-manifolds, including non-homogeneous examples.

Findings

Moduli spaces of nonnegative sectional curvature metrics have infinitely many components.

The s invariant distinguishes different connected components.

Includes examples like Eschenburg and Aloff-Wallach spaces.

Abstract

The Kreck-Stolz s invariant is used to distinguish connected components of the moduli space of positive scalar curvature metrics. We use a formula of Kreck and Stolz to calculate the s invariant for metrics on S^n bundles with nonnegative sectional curvature. We then apply it to show that the moduli spaces of metrics with nonnegative sectional curvature on certain 7-manifolds have infinitely many path components. These include the first non-homogeneous examples of this type and certain positively curved Eschenburg and Aloff-Wallach spaces.