On the topology of the space of Ricci-positive metrics

Botvinnik, Boris; Ebert, Johannes; Wraith, David

doi:10.1090/proc/14988

On the topology of the space of Ricci-positive metrics
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by Boris Botvinnik, Johannes Ebert and David J. Wraith PDF

Proc. Amer. Math. Soc. 148 (2020), 3997-4006 Request permission

Abstract:

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

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