Moduli Spaces of Metrics of Positive Scalar Curvature on Topological Spherical Space Forms

Abstract

Let M be a topological spherical space form, i.e. a smooth manifold whose universal cover is a homotopy sphere. We determine the number of path components of the space and moduli space of Riemannian metrics with positive scalar curvature on M if the dimension of M is at least 5 and M is not simply-connected.

Spaces of positive scalar curvature metrics on totally nonspin manifolds with spin boundary

“…In the case where M is nonspin, but its universal cover is Spin, there are cases where R + (M) is not connected or has even infinitely many path components, see [2,7,8,15,16,23,25]. For totally nonspin manifolds, Kastenholz-Reinhold give an example of a closed, totally nonspin manifold of dimension 6 whose space of psc-metrics has infinitely many components in [21].…”