Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915580081078272 |
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| author | Laubie, Paul |
| author_facet | Laubie, Paul |
| contents | We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads, showing that their augmentation is Cohen-Macaulay and computing its homology. This work answers several open questions asked by Bérénice Delcroix-Oger and Clément Dupont in a recent article. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_23547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets Laubie, Paul Quantum Algebra Algebraic Topology Combinatorics K-Theory and Homology We show a variation of the usual homological freeness criterion for operadic modules over a Koszul operad. We then apply this result to decorated partition posets for some operads, showing that their augmentation is Cohen-Macaulay and computing its homology. This work answers several open questions asked by Bérénice Delcroix-Oger and Clément Dupont in a recent article. |
| title | Homological freeness criterion for operadic modules and application to Cohen-Macalayness of posets |
| topic | Quantum Algebra Algebraic Topology Combinatorics K-Theory and Homology |
| url | https://arxiv.org/abs/2510.23547 |