Homology, Homotopy and Applications

Volume 19 (2017)

Number 2

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

Pages: 61 – 82

DOI: https://dx.doi.org/10.4310/HHA.2017.v19.n2.a4


Rémi Molinier (Department of Mathematics, Kansas State University, Manhattan, Ks., U.S.A.)


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.


fusion system, $p$-local finite group, cohomology with twisted coefficients, group cohomology

2010 Mathematics Subject Classification

20D20, 20J06, 20J15, 55R35, 55R40

Received 15 February 2016

Published 9 August 2017