Spaces of positive intermediate curvature metrics

TL;DR

This paper investigates the topology of spaces of Riemannian metrics with positive intermediate curvature bounds, revealing rich homotopy structures on high-dimensional Spin-manifolds that admit such metrics.

Contribution

It demonstrates that spaces of metrics with positive p-curvature and k-positive Ricci curvature have many non-trivial homotopy groups on certain high-dimensional Spin-manifolds.

Findings

Spaces of positive p-curvature metrics have complex homotopy groups.

High-dimensional Spin-manifolds admit metrics with positive intermediate curvature.

Non-trivial homotopy groups are present in these metric spaces.

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.