Euler Characteristic of Closed Manifolds with Almost Nonnegative Curvature Operator
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866912981570289664 |
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| author | Cai, Jing-Bin |
| author_facet | Cai, Jing-Bin |
| contents | We study closed manifolds with almost nonnegative curvature operator and address a question of Herrmann--Sebastian--Tuschmann concerning the sign of their Euler characteristic. Our main result shows that if a closed $2n$-dimensional manifold admits an almost nonnegative curvature operator together with a uniform upper bound on the curvature operator, then its Euler characteristic is nonnegative. In addition, under an ANCO-type condition and assuming that the fundamental group is infinite, we prove vanishing results for the Euler characteristic, the signature, and, in the spin case, the $\widehat{A}$-genus, extending recent work of Chen--Ge--Han from almost nonnegative Ricci curvature to the curvature-operator setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_23932 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Euler Characteristic of Closed Manifolds with Almost Nonnegative Curvature Operator Cai, Jing-Bin Differential Geometry 53C21 (Primary), 53C20, 53C24 (Secondary) We study closed manifolds with almost nonnegative curvature operator and address a question of Herrmann--Sebastian--Tuschmann concerning the sign of their Euler characteristic. Our main result shows that if a closed $2n$-dimensional manifold admits an almost nonnegative curvature operator together with a uniform upper bound on the curvature operator, then its Euler characteristic is nonnegative. In addition, under an ANCO-type condition and assuming that the fundamental group is infinite, we prove vanishing results for the Euler characteristic, the signature, and, in the spin case, the $\widehat{A}$-genus, extending recent work of Chen--Ge--Han from almost nonnegative Ricci curvature to the curvature-operator setting. |
| title | Euler Characteristic of Closed Manifolds with Almost Nonnegative Curvature Operator |
| topic | Differential Geometry 53C21 (Primary), 53C20, 53C24 (Secondary) |
| url | https://arxiv.org/abs/2603.23932 |