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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.18778 |
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| _version_ | 1866914154684612608 |
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| author | Caputi, Luigi Celoria, Daniele Collari, Carlo |
| author_facet | Caputi, Luigi Celoria, Daniele Collari, Carlo |
| contents | We establish an isomorphism between the 0-degree überhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and some consequences; in particular, we show that überhomology groups detect the standard simplex, and that the double homology's diagonal is related to the connected domination polynomial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_18778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bridging between überhomology and double homology Caputi, Luigi Celoria, Daniele Collari, Carlo Algebraic Topology We establish an isomorphism between the 0-degree überhomology and the double homology of finite simplicial complexes, using a Mayer-Vietoris spectral sequence argument. We clarify the correspondence between these theories by providing examples and some consequences; in particular, we show that überhomology groups detect the standard simplex, and that the double homology's diagonal is related to the connected domination polynomial. |
| title | Bridging between überhomology and double homology |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2406.18778 |