H-Space structures on spaces of metrics of positive scalar curvature

Abstract

We construct and study an $H$-space multiplication on ${\mathcal{R}}^{+}(M)$ for manifolds $M$ which are nullcobordant in their own tangential $2$-type. This is applied to give a rigidity criterion for the action of the diffeomorphism group on ${\mathcal{R}}^{+}(M)$ via pullback. We also compare this to other known multiplicative structures on ${\mathcal{R}}^{+}(M)$.

15 pages, 21 figures; v2: revision according to referee report, accepted for publication in Trans. Amer. Math. Soc

Cited by in corpus (1)

• Spaces of positive intermediate curvature metrics