Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics

Walsh, Mark

doi:10.1090/S0002-9939-2013-11647-3

Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
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Proc. Amer. Math. Soc. 141 (2013), 2475-2484 Request permission

Abstract:

Let $X$ and $Y$ be a pair of smooth manifolds, each obtainable from the other by surgery in codimension at least three. We show that the corresponding spaces ${\mathcal R}{\mathrm i}{\mathrm e}{\mathrm m}^{+}(X)$ and ${\mathcal R}{\mathrm i}{\mathrm e}{\mathrm m}^{+}(Y)$, respectively consisting of Riemannian metrics of positive scalar curvature on $X$ and $Y$, are homotopy equivalent. This result is originally due to V. Chernysh but remains unpublished.

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