On the homotopy type of the space of metrics of positive scalar curvature
Johannes Ebert
Westfälische Wilhelms-Universität Münster, GermanyMichael Wiemeler
Westfälische Wilhelms-Universität Münster, Germany
Abstract
Let be a simply connected spin manifold of dimension admitting Riemannian metrics of positive scalar curvature. Denote by the space of such metrics on . We show that is homotopy equivalent to , where denotes the -dimensional sphere with standard smooth structure.
We also show a similar result for simply connected non-spin manifolds with and . In this case let be the total space of the non-trivial -bundle with structure group over . Then is homotopy equivalent to .
Cite this article
Johannes Ebert, Michael Wiemeler, On the homotopy type of the space of metrics of positive scalar curvature. J. Eur. Math. Soc. (2023), published online first
DOI 10.4171/JEMS/1333