Stable rational cohomology of automorphism groups of free groups and the integral cohomology of moduli spaces of graphs.
It is not known whether or not the stable rational cohomology groups H*(Aut(F);Q) always vanish (see Hatcher in [5] and Hatcher and Vogtmann in [7] where they pose the question and show that it does vanish in the first 6 dimensions). We show that either the rational cohomology does not vanish in certain dimensions, or the integral cohomology of a moduli space of pointed graphs does not stabilize in certain other dimensions. Similar results are stated for groups of outer automorphisms. This yields...