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

Frenck, Georg

doi:10.1090/tran/8505

$H$-Space structures on spaces of metrics of positive scalar curvature
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Trans. Amer. Math. Soc. 374 (2021), 8989-9006 Request permission

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 ${\mathcal {R}}^+(M)$.

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