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

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https://ir.library.oregonstate.edu/concern/articles/pr76f492j

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  • 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 This result is originally due to V. Chernysh but remains unpublished.
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  • Walsh, M. (2013). Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics. Proceedings of the American Mathematical Society, 141(7), 2475-2484. doi:10.1090/S0002-9939-2013-11647-3
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  • 141
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  • 7
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