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

Georg Frenck

doi:10.1090/tran/8505

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arXiv · 2004.01033

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

Georg Frenck

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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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Georg Frenck. 2020-04-02. H-Space structures on spaces of metrics of positive scalar curvature. https://doi.org/10.1090/tran/8505

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