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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.05174 |
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| _version_ | 1866929337801900032 |
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| author | Williams, Brian R |
| author_facet | Williams, Brian R |
| contents | We compute the local cohomology of vector fields on a manifold. In the smooth case this recovers the diagonal cohomology studied in work of Losik, Guillemin, Fuks and others. In the holomorphic case this cohomology has recently appeared in work of Hennion and Kapranov in their study of the Lie algebra cohomology of vector fields on a complex manifold. Additionally, we construct explicit representatives for cocycles in Gelfand--Fuks cohomology via descent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05174 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The local cohomology of vector fields Williams, Brian R Differential Geometry High Energy Physics - Theory Algebraic Geometry We compute the local cohomology of vector fields on a manifold. In the smooth case this recovers the diagonal cohomology studied in work of Losik, Guillemin, Fuks and others. In the holomorphic case this cohomology has recently appeared in work of Hennion and Kapranov in their study of the Lie algebra cohomology of vector fields on a complex manifold. Additionally, we construct explicit representatives for cocycles in Gelfand--Fuks cohomology via descent. |
| title | The local cohomology of vector fields |
| topic | Differential Geometry High Energy Physics - Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2405.05174 |