Cohomology with twisted coefficients of the classifying space of a fusion system

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• 作者：Ré ; mi Molinier ^{molinier@math.univ-paris13.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：55R40 ; 55N25 ; 55R35 ; 20J06 ; 20D20 ; 20J15
• 刊名：Topology and its Applications
• 出版年：2016
• 出版时间：1 October 2016
• 年：2016
• 卷：212
• 期：Complete
• 页码：1-18
• 全文大小：428 K

文摘

We study the cohomology with twisted coefficients of the geometric realization of a linking system associated to a saturated fusion system F$\mathcal{F}$. More precisely, we extend a result due to Broto, Levi and Oliver to twisted coefficients. We generalize the notion of F$\mathcal{F}$-stable elements to 2017d37fa8381656e08" title="Click to view the MathML source">F^c${\mathcal{F}}^c$-stable elements in a setting of cohomology with twisted coefficients by an action of the fundamental group. We then study the problem of inducing an idempotent from an F$\mathcal{F}$-characteristic 205a272bb6ececa54a119327" title="Click to view the MathML source">(S,S)$(S,S)$-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 2017d37fa8381656e08" title="Click to view the MathML source">F^c${\mathcal{F}}^c$-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 2017d37fa8381656e08" title="Click to view the MathML source">F^c${\mathcal{F}}^c$-stable elements.