Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909479246757888 |
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| author | Wade, Richard D. Wasserman, Thomas A. |
| author_facet | Wade, Richard D. Wasserman, Thomas A. |
| contents | We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincaré Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working knowledge of simplicial complexes and (co)homology. The main motivation is a link with Bieri-Eckmann duality for discrete groups, which is explored in a companion paper. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_05873 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves Wade, Richard D. Wasserman, Thomas A. Algebraic Topology Group Theory 55M05, 55N30 (Primary) 55T25, 55U10 (Secondary) We prove a duality theorem for Cohen--Macaulay simplicial complexes. This is a generalisation of Poincaré Duality, framed in the language of combinatorial sheaves. Our treatment is self-contained and accessible for readers with a working knowledge of simplicial complexes and (co)homology. The main motivation is a link with Bieri-Eckmann duality for discrete groups, which is explored in a companion paper. |
| title | Duality for Cohen--Macaulay Complexes through Combinatorial Sheaves |
| topic | Algebraic Topology Group Theory 55M05, 55N30 (Primary) 55T25, 55U10 (Secondary) |
| url | https://arxiv.org/abs/2405.05873 |