Spaces of positive intermediate curvature metrics

Abstract

AbstractIn this paper we study spaces of Riemannian metrics with lower bounds on intermediate curvatures. We show that the spaces of metrics of positive p-curvature and k-positive Ricci curvature on a given high-dimensional $$\mathrm {Spin}$$ Spin -manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.