On the topology of the space of Ricci-positive metrics

Abstract

We show that the space ${\mathcal{R}}^{\mathrm{pRc}}(W_g^{2n})$ of metrics with positive Ricci curvature on the manifold $W_g^{2n}:={♯}^g(S^n\times S^n)$ has nontrivial rational homology if $n\not\equiv 3(\mathrm{mod}4)$ and $g$ are both sufficiently large. The same argument applies to ${\mathcal{R}}^{\mathrm{pRc}}(W_g^{2n}♯N)$ provided that $N$ is spin and $W_g^{2n}♯N$ admits a Ricci positive metric.

arXiv commentFinal version, to appear in Proceedings of the AMS