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

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 cuvature 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 which includes $(2n-2)$-connected $(4n-2)$-dimensional manifolds, then the fundamental group of ${\mathcal{M}}_0^{+}(M)$ is non-trivial.

14 pages; minor changes; to appear in IMRN

References in corpus (2)

• Infinite loop spaces and positive scalar curvature
• Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets

Cited by in corpus (1)

• On the topology of moduli spaces of non-negatively curved Riemannian metrics