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arXiv · 1507.02401

Cohomology of linking systems with twisted coefficients by a $p$-solvable action

Rémi Molinier
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Abstract

In this paper we study the cohomology of the geometric realization of linking systems with twisted coefficients. More precisely, given a prime $p$ and a $p$-local finite group $(S,\mathcal{F},\mathcal{L})$, we compare the cohomology of $\mathcal{L}$ with twisted coefficients with the submodule of $\mathcal{F}^c$-stable elements in the cohomology of $S$. We start with the particular case of constrained fusion systems. Then, we study the case of $p$-solvable actions on the coefficients.

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Rémi Molinier. 2015-07-09. Cohomology of linking systems with twisted coefficients by a $p$-solvable action. https://doi.org/10.4310/hha.2017.v19.n2.a4

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