On the moduli spaces of metrics with nonnegative sectional curvature
Differential Geometry
2020-11-13 v3
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.
Keywords
Cite
@article{arxiv.1712.01107,
title = {On the moduli spaces of metrics with nonnegative sectional curvature},
author = {McFeely Jackson Goodman},
journal= {arXiv preprint arXiv:1712.01107},
year = {2020}
}
Comments
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