Gardado en:
| Main Authors: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| Subjects: | |
| Acceso en liña: | https://arxiv.org/abs/2012.00432 |
| Tags: |
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Table of Contents:
- Let $M^d$ be a simply connected spin manifold of dimension $d \geq 5$ admitting Riemannian metrics of positive scalar curvature. Denote by $\mathcal{R}^+(M^d)$ the space of such metrics on $M^d$. We show that $\mathcal{R}^+(M^d)$ is homotopy equivalent to $\mathcal{R}^+(S^d)$, where $S^d$ denotes the $d$-dimensional sphere with standard smooth structure. We also show a similar result for simply connected non-spin manifolds $M^d$ with $d\geq 5$ and $d\neq 8$. In this case let $W^d$ be the total space of the non-trivial $S^{d-2}$-bundle with structure group $SO(d-1)$ over $S^2$. Then $\mathcal{R}^+(M^d)$ is homotopy equivalent to $\mathcal{R}^+(W^d)$.