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

Abstract

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