HOCHSCHILD-PIRASHVILI HOMOLOGY ON SUSPENSIONS AND REPRESENTATIONS OF Out (Fn)

We show that the Hochschild-Pirashvili homology on any suspension admits the so called Hodge splitting. For a map between suspensions f: Sigma Y -> Sigma Z, the induced map in the Hochschild-Pirashvili homology preserves this splitting if f is a suspension. If f is not a suspension, we show that the splitting is preserved only as a filtration. As a special case, we obtain that the Hochschild-Pirashvili homology on wedges of circles produces new representations of Out(F-n) that do not factor in general through GL(n, Z). The obtained representations are naturally filtered in such a way that the action on the graded quotients does factor through GL(n, Z).