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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.03499 |
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| _version_ | 1866913976326029312 |
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| author | Huber, Annette Kaiser, Tobias Oswal, Abhishek |
| author_facet | Huber, Annette Kaiser, Tobias Oswal, Abhishek |
| contents | For globally subanalytic manifolds we define de Rham complexes of globally subanalytic differential forms and of constructible differential forms. Whereas the de Rham theorem does not hold for the former in the non-compact case, it does hold for the latter in full generality. We deduce that the constructible de Rham cohomology groups are canonically isomorphic to the classical ones. We stress that our results apply already in the $C^1$-setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the de Rham theorem in the globally subanalytic setting Huber, Annette Kaiser, Tobias Oswal, Abhishek Logic Classical Analysis and ODEs Complex Variables 03C64, 32B20, 32C05, 58A07, 58A12 For globally subanalytic manifolds we define de Rham complexes of globally subanalytic differential forms and of constructible differential forms. Whereas the de Rham theorem does not hold for the former in the non-compact case, it does hold for the latter in full generality. We deduce that the constructible de Rham cohomology groups are canonically isomorphic to the classical ones. We stress that our results apply already in the $C^1$-setting. |
| title | On the de Rham theorem in the globally subanalytic setting |
| topic | Logic Classical Analysis and ODEs Complex Variables 03C64, 32B20, 32C05, 58A07, 58A12 |
| url | https://arxiv.org/abs/2508.03499 |