THE DEHN FUNCTIONS OF Out(Fn) AND Aut(Fn)

For n at least 3, the Dehn functions of Out(F-n) and Aut(F-n) are exponentia. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n = 3 was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for n bigger than 3 to the case n = 3. In this note we give a shorter, more direct proof of this last reduction.