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

TL;DR
This paper investigates the topological structure of the space of Ricci-positive metrics on certain high-dimensional manifolds, revealing nontrivial rational homology under specific conditions related to the manifold's genus and dimension.
Contribution
It demonstrates the existence of nontrivial rational homology in the space of Ricci-positive metrics on connected sums of spheres, extending to manifolds with additional spin structures.
Findings
Nontrivial rational homology in the space of Ricci-positive metrics for large genus and specific dimensions.
Applicability of the results to manifolds with spin structures and Ricci-positive metrics.
Conditions on dimension and genus for the topological complexity of the metric space.
Abstract
We show that the space of metrics with positive Ricci curvature on the manifold has nontrivial rational homology if and are both sufficiently large. The same argument applies to provided that is spin and admits a Ricci positive metric.
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