On moduli spaces of positive scalar curvature metrics on highly connected manifolds

Wiemeler, Michael

Abstract

Let M be a simply connected spin manifold of dimension at least six, which admits a metric of positive scalar curvature. We show that the observer moduli space of positive scalar curvature metrics on M  has non-trivial higher homotopy groups. Moreover, denote by \mathcal{M}_0^+(M) the moduli space of positive scalar curvature metrics on M associated to the group of orientation-preserving diffeomorphisms of M⁠. We show that if M belongs to a certain class of manifolds that includes (2n-2)-connected (4n-2)-dimensional manifolds, then the fundamental group of \mathcal{M}_0^+(M) is non-trivial.