On the moduli spaces of metrics with nonnegative sectional curvature

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.

14 pages; v2: proofs are simplified, and new examples added, specifically S^3 bundles over S^4 and CP^2, v3: new examples added, including certain positively curved Eschenburg and Aloff-Wallach spaces