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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2505.20599 |
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| _version_ | 1866915306026303488 |
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| author | Jiang, Huihong |
| author_facet | Jiang, Huihong |
| contents | We construct a family of examples of complete $(2+n)-$dimensional ($n\ge 2$) open manifolds with positive Ricci curvature, sectional curvature bounded from below and infinite Betti numbers $b_2,b_n$, moreover its volume growth can be arbitrarily close to quadratic volume growth. Compared with some known result of finite topology for manifolds with nonnegative Ricci curvature and lower sectional curvature bound, it makes sense to ask whether complete manifolds with such curvature bounds must be of finite topological type or not provided with at most quadratic volume growth. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20599 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Examples of open manifolds with almost quadratic volume growth and infinite Betti numbers Jiang, Huihong Differential Geometry We construct a family of examples of complete $(2+n)-$dimensional ($n\ge 2$) open manifolds with positive Ricci curvature, sectional curvature bounded from below and infinite Betti numbers $b_2,b_n$, moreover its volume growth can be arbitrarily close to quadratic volume growth. Compared with some known result of finite topology for manifolds with nonnegative Ricci curvature and lower sectional curvature bound, it makes sense to ask whether complete manifolds with such curvature bounds must be of finite topological type or not provided with at most quadratic volume growth. |
| title | Examples of open manifolds with almost quadratic volume growth and infinite Betti numbers |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2505.20599 |