On the computation of coarse cohomology
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910287375892480 |
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| author | Banerjee, Arka |
| author_facet | Banerjee, Arka |
| contents | The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the boundedly supported cohomology. Boundedly supported cohomology coincides with compactly supported Alexander--Spanier cohomology if the space is proper and contractible. Our work generalizes an earlier result of Roe which says that the coarse cohomology is isomorphic to the compactly supported Alexander-Spanier cohomology if the space is uniformly contractible. As an application of our main theorem, we obtain that coarse cohomology of the complement can be computed in terms of Alexander-Spanier cohomology for many spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02231 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the computation of coarse cohomology Banerjee, Arka Metric Geometry The purpose of this article is to relate coarse cohomology of metric spaces with a more computable cohomology. We introduce a notion of boundedly supported cohomology and prove that coarse cohomology of many spaces are isomorphic to the boundedly supported cohomology. Boundedly supported cohomology coincides with compactly supported Alexander--Spanier cohomology if the space is proper and contractible. Our work generalizes an earlier result of Roe which says that the coarse cohomology is isomorphic to the compactly supported Alexander-Spanier cohomology if the space is uniformly contractible. As an application of our main theorem, we obtain that coarse cohomology of the complement can be computed in terms of Alexander-Spanier cohomology for many spaces. |
| title | On the computation of coarse cohomology |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2401.02231 |