# Cohomology of automorphism groups of free groups with twisted coefficients

Randal-Williams, Oscar

Article

We compute the groups H*(Aut(F\$_{n}\$);M) and H*(Out(F\$_{n}\$);M) in a stable range, where M is obtained by applying a Schur functor to H\$_{Q}\$ or H\$_{Q}\$, respectively the first rational homology and cohomology of F\$_{n}\$. The answer may be described in terms of stable multiplicities of irreducibles in the plethysm Sym\$^{k}\$ \$\circ\$ Sym\$^{l}\$ of symmetric powers. We also compute the stable integral cohomology groups of Aut(F\$_{n}\$) with coefficients in H or H*.