Cohomology of linking systems with twisted coefficients by a $p$-solvable action - Archive ouverte HAL Access content directly
Journal Articles Homology, Homotopy and Applications Year : 2017

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

Rémi Molinier

Abstract

In this paper we study the cohomology of the geometric realization of linking systems with coefficients twisted by a $p$-solvable action. More precisely, we try to compare it with the submodule of $\mathcal{F}$-stable elements in the cohomology of the Sylow. The main tools we use is the notion of $p$-local subgroup of index a power of $p$ or prime to $p$. We first study extension by a $p'$-group in a general setting. We give some results for any $p$-solvable action in the case of realizable $p$-local finite groups and make a conjecture that this could be generalized to any $p$-local finite groups. We finally give some constructions and examples to study this conjecture.
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Dates and versions

hal-02280278 , version 1 (20-02-2024)

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Rémi Molinier. Cohomology of linking systems with twisted coefficients by a $p$-solvable action. Homology, Homotopy and Applications, 2017, 19 (2), pp.61-82. ⟨10.4310/HHA.2017.v19.n2.a4⟩. ⟨hal-02280278⟩

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