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Quantifying Quillen’s uniform $\mathcal{F}_p$-isomorphism theorem
Homology, Homotopy and Applications ( IF 0.5 ) Pub Date : 2020-01-01 , DOI: 10.4310/hha.2020.v22.n2.a4
Koenraad van Woerden

Let $G$ be a finite group with $2$-Sylow subgroup of order less than or equal to 16. For such a $G$, we prove a quantified version of Quillen's uniform $\mathcal{F}_p$-isomorphism theorem, which holds uniformly for all $G$-spaces. We do this by bounding from above the exponent of Borel equivariant $\mathbf{F}_2$-cohomology, as introduced by Mathew-Naumann-Noel, with respect to the family of elementary abelian 2-subgroups.

中文翻译:

量化 Quillen 的统一 $\mathcal{F}_p$-同构定理

令$G$是一个有限群,其阶数小于或等于16的$2$-Sylow子群。对于这样的$G$,我们证明了Quillen统一$\mathcal{F}_p$-同构定理的量化版本,对于所有 $G$-spaces 都是一致的。我们通过从 Mathew-Naumann-Noel 引入的关于基本阿贝尔 2-子群族的 Borel 等变 $\mathbf{F}_2$-上同调的指数上界来做到这一点。
更新日期:2020-01-01
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