Filtered complexes and cohomologically equivalent subcomplexes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866911201963802624 |
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| author | Grong, Erlend Tripaldi, Francesca |
| author_facet | Grong, Erlend Tripaldi, Francesca |
| contents | Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is cohomologically equivalent to the de Rham complex, we present a more general construction that produces subcomplexes from any filtered cochain complex of finite depth and still computes the cohomology of the original filtered complex. A priori these subcomplexes depend not only on the filtration itself, but also on the choice of additional structures. However, we show that the construction only depends on the given filtration up to isomorphism. Finally, we show how such subcomplexes relate to spectral sequences, a cohomological machinery that arises naturally when considering a filtered complex. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_11353 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Filtered complexes and cohomologically equivalent subcomplexes Grong, Erlend Tripaldi, Francesca Differential Geometry Algebraic Topology 57R19, 55T10, 16W70, 53C17 Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is cohomologically equivalent to the de Rham complex, we present a more general construction that produces subcomplexes from any filtered cochain complex of finite depth and still computes the cohomology of the original filtered complex. A priori these subcomplexes depend not only on the filtration itself, but also on the choice of additional structures. However, we show that the construction only depends on the given filtration up to isomorphism. Finally, we show how such subcomplexes relate to spectral sequences, a cohomological machinery that arises naturally when considering a filtered complex. |
| title | Filtered complexes and cohomologically equivalent subcomplexes |
| topic | Differential Geometry Algebraic Topology 57R19, 55T10, 16W70, 53C17 |
| url | https://arxiv.org/abs/2308.11353 |