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arXiv · 2302.06160

Generalized Periodicity in Group Cohomology

Nir Elber
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Abstract

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.

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Nir Elber. 2023-02-13. Generalized Periodicity in Group Cohomology. https://doi.org/10.1080/00927872.2023.2296883

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