Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
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Walsh, Mark. 2013. Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics. Proceedings of the American Mathematical Society, vol. 141:no. 7:pp. 2475-2484,Article no. PII S 0002-9939(2013)11647-3
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 Riem(+)(X) and Riem(+)(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 This result is originally due to V. Chernysh but remains unpublished.
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