Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
Citation
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
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 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 This result is originally due to V. Chernysh but remains unpublished.
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