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Moduli spaces of Ricci positive metrics in dimension five

McFeely Jackson Goodman

Geometry & Topology 28 (2024) 1065–1098
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 S1 bundles over #aP2 # bP2¯ and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5–manifolds with fundamental group 2 admitting free S1 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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