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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2411.03882 |
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| _version_ | 1866909750330916864 |
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| author | Tony, Thomas |
| author_facet | Tony, Thomas |
| contents | Every closed connected Riemannian spin manifold of non-zero $\hat{A}$-genus or non-zero Hitchin invariant with non-negative scalar curvature admits a parallel spinor, in particular is Ricci-flat. In this note, we generalize this result to closed connected spin manifolds of non-vanishing Rosenberg index. This provides a criterion for the existence of a parallel spinor on a finite covering and yields that every closed connected Ricci-flat spin manifold of dimension $\geq 2$ with non-vanishing Rosenberg index has special holonomy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03882 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index Tony, Thomas Differential Geometry K-Theory and Homology Every closed connected Riemannian spin manifold of non-zero $\hat{A}$-genus or non-zero Hitchin invariant with non-negative scalar curvature admits a parallel spinor, in particular is Ricci-flat. In this note, we generalize this result to closed connected spin manifolds of non-vanishing Rosenberg index. This provides a criterion for the existence of a parallel spinor on a finite covering and yields that every closed connected Ricci-flat spin manifold of dimension $\geq 2$ with non-vanishing Rosenberg index has special holonomy. |
| title | Ricci-Flat Manifolds, Parallel Spinors and the Rosenberg Index |
| topic | Differential Geometry K-Theory and Homology |
| url | https://arxiv.org/abs/2411.03882 |