On the topology of moduli spaces of non-negatively curved Riemannian metrics

Abstract

We study spaces and moduli spaces of Riemannian metrics with non-negative Ricci or non-negative sectional curvature on closed and open manifolds. We construct, in particular, the first classes of manifolds for which these moduli spaces have non-trivial rational homotopy, homology and cohomology groups. We also show that in every dimension at least seven (respectively, at least eight) there exist closed (respectively, open) manifolds for which the space and moduli space of Riemannian metrics with non-negative sectional curvature has infinitely many path components. A completely analogous statement holds for spaces and moduli spaces of non-negative Ricci curvature metrics.

26 pages; minor changes; accepted for publication in Math. Ann

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Cited by in corpus (3)

• Moduli space of nonnegatively curved metrics on manifolds of dimension $4k+1$
• Moduli spaces of compact RCD(0,N)-structures
• Moduli space of metrics of nonnegative sectional or positive Ricci curvature on Brieskorn quotients in dimension 5