Vector fields on non-compact manifolds
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929634230140928 |
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| author | Kato, Tsuyoshi Kishimoto, Daisuke Tsutaya, Mitsunobu |
| author_facet | Kato, Tsuyoshi Kishimoto, Daisuke Tsutaya, Mitsunobu |
| contents | Let $M$ be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group $G$. We establish a Poincaré-Hopf theorem for a bounded vector field on $M$ satisfying a mild condition on zeros. As an application, we show that such a vector field must have infinitely many zeros whenever $G$ is amenable and the Euler characteristic of $M/G$ is non-zero. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_00512 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Vector fields on non-compact manifolds Kato, Tsuyoshi Kishimoto, Daisuke Tsutaya, Mitsunobu Geometric Topology Algebraic Topology Differential Geometry 57R25, 58K45 Let $M$ be a non-compact connected manifold with a cocompact and properly discontinuous action of a discrete group $G$. We establish a Poincaré-Hopf theorem for a bounded vector field on $M$ satisfying a mild condition on zeros. As an application, we show that such a vector field must have infinitely many zeros whenever $G$ is amenable and the Euler characteristic of $M/G$ is non-zero. |
| title | Vector fields on non-compact manifolds |
| topic | Geometric Topology Algebraic Topology Differential Geometry 57R25, 58K45 |
| url | https://arxiv.org/abs/2211.00512 |