Moduli spaces of Ricci positive metrics in dimension five

Goodman, McFeely Jackson

doi:10.2140/gt.2024.28.1065

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Moduli spaces of Ricci positive metrics in dimension five

McFeely Jackson Goodman

Geometry & Topology 28 (2024) 1065–1098

DOI: 10.2140/gt.2024.28.1065

Abstract

We use the $η$ 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 nondiffeomorphic five-dimensional manifolds for which these moduli spaces each have infinitely many components. The manifolds are total spaces of principal $S^{1}$ bundles over $#^{a} ℂ P^{2} #^{b} \bar{ℂ P^{2}}$ and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify $5$ –manifolds with fundamental group $ℤ_{2}$ admitting free $S^{1}$ actions with simply connected quotients.

Keywords

moduli spaces, positive Ricci curvature

Mathematical Subject Classification

Primary: 53C20, 53C27, 58D19, 58D27, 58J28

Secondary: 19K56

References

Publication

Received: 4 December 2020

Revised: 1 April 2022

Accepted: 28 July 2022

Published: 10 May 2024

Proposed: Tomasz S Mrowka

Seconded: Tobias H Colding, David Fisher

Authors

McFeely Jackson Goodman
Department of Mathematics Colby College Waterville, ME United States

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Volume 28, issue 3 (2024)