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Moduli space of metrics of nonnegative sectional or positive Ricci curvature on homotopy real projective spaces. (English) Zbl 1477.53058

Authors’ abstract: We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy \(\mathbb{R} P^5\) has infinitely many path components. We also show that in each dimension \(4k+1\) there are at least \(2^{2k}\) homotopy \(\mathbb{R} P^{4k+1} \)’s of pairwise distinct oriented diffeomorphism type for which the moduli space of metrics of positive Ricci curvature has infinitely many path components. Examples of closed manifolds with finite fundamental group with these properties were known before only in dimensions \(4k+3\geq 7\).

MSC:

53C20 Global Riemannian geometry, including pinching
58D27 Moduli problems for differential geometric structures
58J28 Eta-invariants, Chern-Simons invariants
19K56 Index theory
57R55 Differentiable structures in differential topology
53C27 Spin and Spin\({}^c\) geometry
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