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arXiv · 2002.00333

Moduli spaces of Ricci positive metrics in dimension five

McFeely Jackson Goodman
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Abstract

We use the $\eta$ invariants of spin$^c$ Dirac operators to distinguish connected components of moduli spaces of Riemannian metrics with positive Ricci curvature. We then find infinitely many non-diffeomorphic five dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal $S^1$ bundles over $\#^a\mathbb{C}P^2\#^b\overline{\mathbb{C}P^2}$ and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5-manifolds with fundamental group $\mathbb{Z}_2$ admitting free $S^1$ actions with simply connected quotients.

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McFeely Jackson Goodman. 2020-02-02. Moduli spaces of Ricci positive metrics in dimension five. https://doi.org/10.2140/gt.2024.28.1065

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