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We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...

For $n$ at least 3, the Dehn functions of $Out\left(F_n\right)$ and $Aut\left(F_n\right)$ are exponential. 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.