Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866910194265489408 |
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| author | He, Fei |
| author_facet | He, Fei |
| contents | This paper proves several topological results for smooth gradient Ricci shrinkers. We establish upper bounds for the Betti numbers, a vanishing theorem for cohomology, and a dichotomy for the number of ends. We also prove a full Hodge theorem for a large class of shrinkers. The methods are based on weighted $L^2$ cohomology and extend to self-shrinkers of the mean curvature flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_04476 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology He, Fei Differential Geometry Analysis of PDEs This paper proves several topological results for smooth gradient Ricci shrinkers. We establish upper bounds for the Betti numbers, a vanishing theorem for cohomology, and a dichotomy for the number of ends. We also prove a full Hodge theorem for a large class of shrinkers. The methods are based on weighted $L^2$ cohomology and extend to self-shrinkers of the mean curvature flow. |
| title | Topology of gradient Ricci shrinkers via weighted $L^2$ cohomology |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2605.04476 |