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arXiv · 1712.01107

On the moduli spaces of metrics with nonnegative sectional curvature

McFeely Jackson Goodman
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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.

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McFeely Jackson Goodman. 2017-12-04. On the moduli spaces of metrics with nonnegative sectional curvature. https://doi.org/10.1007/s10455-020-09700-1

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