English

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