Poincaré's lemma for formal manifolds
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917744161587200 |
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| author | Chen, Fulin Sun, Binyong Wang, Chuyun |
| author_facet | Chen, Fulin Sun, Binyong Wang, Chuyun |
| contents | This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds, including generalizations of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. In this paper, we establish Poincaré's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04263 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Poincaré's lemma for formal manifolds Chen, Fulin Sun, Binyong Wang, Chuyun Functional Analysis Differential Geometry This is a paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In two previous papers, we develop the basic theory of formal manifolds, including generalizations of vector-valued distributions and generalized functions on smooth manifolds to the setting of formal manifolds. In this paper, we establish Poincaré's lemma for de Rham complexes with coefficients in formal functions, formal generalized functions, compactly supported formal densities, or compactly supported formal distributions. |
| title | Poincaré's lemma for formal manifolds |
| topic | Functional Analysis Differential Geometry |
| url | https://arxiv.org/abs/2408.04263 |