Spaces of positive intermediate curvature metrics

DOI10.1007/S10711-021-00635-WzbMath1518.58007arXiv2011.11388MaRDI QIDQ6354340

Publication date: 23 November 2020

Abstract: In 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 Spin-manifold have many non-trivial homotopy groups provided that the manifold admits such a metric.

Mathematics Subject Classification ID

Characteristic classes and numbers in differential topology (57R20) Groups of diffeomorphisms and homeomorphisms as manifolds (58D05) Surgery and handlebodies (57R65) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Other types of cobordism (57R90) Manifolds of metrics (especially Riemannian) (58D17)

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