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• W2102620906 abstract "We study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system $mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver to twisted coefficients. We generalize the notion of $mathcal{F}$-stable elements to $mathcal{F}^c$-stable elements in a setting of cohomology with twisted coefficients by an action of the fundamental group.% or, in other word, with locally constant coefficients. We then study the problem of inducing an idempotent from an $mathcal{F}$-characteristic $(S,S)$-biset and we show that, if the coefficient module is nilpotent, then the cohomology of the geometric realization of a linking system can be computed by $mathcal{F}^c$-stable elements. As a corollary, we show that for any coefficient module, the cohomology of the classifying space of a $p$-local finite group can be computed by these $mathcal{F}^c$-stable elements." @default.
• W2102620906 created "2016-06-24" @default.
• W2102620906 creator A5018407485 @default.
• W2102620906 date "2016-10-01" @default.
• W2102620906 modified "2023-09-30" @default.
• W2102620906 title "Cohomology with twisted coefficients of the classifying space of a fusion system" @default.
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• W2102620906 doi "https://doi.org/10.1016/j.topol.2016.09.001" @default.
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