Topology of singular foliations of closed 1-forms on orbifolds
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910098389991424 |
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| author | Garcia, Daniel Lopez Valencia, Fabricio |
| author_facet | Garcia, Daniel Lopez Valencia, Fabricio |
| contents | We study the topological properties of the leaves of the singular foliation induced by a closed 1-form of Morse type on a compact orbifold. In particular, we establish criteria that characterize when all such leaves are compact, when they are non-compact, and how both types may coexist. As an application, we extend to the orbifold setting a celebrated result of Calabi, which provides a purely topological characterization of intrinsically closed harmonic 1-forms of Morse type. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_09644 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Topology of singular foliations of closed 1-forms on orbifolds Garcia, Daniel Lopez Valencia, Fabricio Differential Geometry Geometric Topology 22A22, 57R18, 57R70 We study the topological properties of the leaves of the singular foliation induced by a closed 1-form of Morse type on a compact orbifold. In particular, we establish criteria that characterize when all such leaves are compact, when they are non-compact, and how both types may coexist. As an application, we extend to the orbifold setting a celebrated result of Calabi, which provides a purely topological characterization of intrinsically closed harmonic 1-forms of Morse type. |
| title | Topology of singular foliations of closed 1-forms on orbifolds |
| topic | Differential Geometry Geometric Topology 22A22, 57R18, 57R70 |
| url | https://arxiv.org/abs/2507.09644 |