Sur l'application de Quillen pour la cohomologie modulo 2 de certains groupes finis
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913639410171904 |
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| author | Lannes, Jean |
| author_facet | Lannes, Jean |
| contents | Let $G$ be a finite group. In a famous article, Quillen describes an $\mathrm{F}$-isomorphism between commutative $\mathbb{N}$-graded $\mathbb{F}_{2}$-algebras $$\mathrm{q}_{G}:\mathrm{H}^{*}(G;\mathbb{F}_{2})\to\mathrm{L}(G)\ ,$$ with $\mathrm{L}(G)$ defined in terms of the elementary abelian $2$-groups contained in $G$. We show that $\mathrm{q}_{G}$ is in fact an actual isomorphism for three families of finite groups: symmetric groups, alternating groups and finite Coxeter groups. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_03953 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sur l'application de Quillen pour la cohomologie modulo 2 de certains groupes finis Lannes, Jean Algebraic Topology Let $G$ be a finite group. In a famous article, Quillen describes an $\mathrm{F}$-isomorphism between commutative $\mathbb{N}$-graded $\mathbb{F}_{2}$-algebras $$\mathrm{q}_{G}:\mathrm{H}^{*}(G;\mathbb{F}_{2})\to\mathrm{L}(G)\ ,$$ with $\mathrm{L}(G)$ defined in terms of the elementary abelian $2$-groups contained in $G$. We show that $\mathrm{q}_{G}$ is in fact an actual isomorphism for three families of finite groups: symmetric groups, alternating groups and finite Coxeter groups. |
| title | Sur l'application de Quillen pour la cohomologie modulo 2 de certains groupes finis |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2501.03953 |