Cohomology of automorphism groups of free groups with twisted coefficients

Abstract

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*.