Cobordism invariance of the homotopy type of the space of positive scalar curvature metrics
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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 This result is originally due to V. Chernysh but remains unpublished.References
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Additional Information
- Mark Walsh
- Affiliation: Department of Mathematics, Oregon State University, Corvallis, Oregon 97331
- Address at time of publication: Department of Mathematics, Statistics and Physics, Wichita State University, Wichita, Kansas 67260
- Email: walsh@math.wichita.edu
- Received by editor(s): October 10, 2011
- Published electronically: February 21, 2013
- Communicated by: Daniel Ruberman
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 141 (2013), 2475-2484
- MSC (2010): Primary 53C21, 55P10
- DOI: https://doi.org/10.1090/S0002-9939-2013-11647-3
- MathSciNet review: 3043028