On the topology of the space of Ricci-positive metrics

2018/09/28 by Botvinnik, Boris, Ebert, Johannes, Wraith, David J.
#Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1809.11050

Abstract

We show that the space R^pRc(W_g²ⁿ) of metrics with positive Ricci curvature on the manifold W²ⁿ_g := \sharp^g (Sⁿ × Sⁿ) has nontrivial rational homology if n \not ≡ 3 \pmod 4 and g are both sufficiently large. The same argument applies to R^pRc(W_g²ⁿ \sharp N) provided that N is spin and W_g²ⁿ \sharp N admits a Ricci positive metric.

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