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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Mark Walsh
Journal: Proc. Amer. Math. Soc. 141 (2013), 2475-2484
MSC (2010): Primary 53C21, 55P10
Published electronically: February 21, 2013
MathSciNet review: 3043028
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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 This result is originally due to V. Chernysh but remains unpublished.


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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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11647-3
PII: S 0002-9939(2013)11647-3
Received by editor(s): October 10, 2011
Published electronically: February 21, 2013
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.