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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2302.06160 |
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| _version_ | 1866913181312483328 |
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| author | Elber, Nir |
| author_facet | Elber, Nir |
| contents | Given a finite group $G$, we introduce "encoding pairs," which are a pair of $G$-modules $M$ and $M'$ equipped with a shifted natural isomorphism between the cohomological functors $H^\bullet(G,\mathrm{Hom}_\mathbb Z(M,-))$ and $H^\bullet(G,\mathrm{Hom}_\mathbb Z(M',-))$. Studying these encoding pairs generalizes the theory of periodic cohomology for finite groups, allowing us to generalize the cohomological input of a theorem due to Swan that roughly says that a finite group with periodic cohomology acts feely on some sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_06160 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Generalized Periodicity in Group Cohomology Elber, Nir Group Theory 20J06 Given a finite group $G$, we introduce "encoding pairs," which are a pair of $G$-modules $M$ and $M'$ equipped with a shifted natural isomorphism between the cohomological functors $H^\bullet(G,\mathrm{Hom}_\mathbb Z(M,-))$ and $H^\bullet(G,\mathrm{Hom}_\mathbb Z(M',-))$. Studying these encoding pairs generalizes the theory of periodic cohomology for finite groups, allowing us to generalize the cohomological input of a theorem due to Swan that roughly says that a finite group with periodic cohomology acts feely on some sphere. |
| title | Generalized Periodicity in Group Cohomology |
| topic | Group Theory 20J06 |
| url | https://arxiv.org/abs/2302.06160 |