A stability conjecture for the unstable cohomology of SL_n(Z), mapping class groups, and Aut(F_n) (with T. Church and B. Farb) - [pdf] [ps]
preprint 2012, submitted.

Abstract :
In this paper we give a conjectural picture of a large piece of the unstable rational cohomology of SL_n(Z), of mapping class groups, and of Aut(F_n).