An $\protect \text{HP}^2$-bundle over $\protect \text{S}^4$ with nontrivial Â-genus
We explain the existence of a smooth $\mathbf{H} P^2$-bundle over $S^4$ whose total space has nontrivial $\hat{A}$-genus. Combined with an argument going back to Hitchin, this answers a question of Schick and implies that the space of Riemannian metrics of positive sectional curvature on a closed ma...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Académie des sciences
2021-03-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.156/ |
| Summary: | We explain the existence of a smooth $\mathbf{H} P^2$-bundle over $S^4$ whose total space has nontrivial $\hat{A}$-genus. Combined with an argument going back to Hitchin, this answers a question of Schick and implies that the space of Riemannian metrics of positive sectional curvature on a closed manifold can have nontrivial higher rational homotopy groups. |
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| ISSN: | 1778-3569 |