Right-angled Artin groups and Out(F_n) I: quasi-isometric embeddings

We construct quasi-isometric embeddings from right-angled Artin groups into the outer automorphism group of a free group. These homomorphisms are in analogy with those constructed in \cite{CLM}, where the target group is the mapping class group of a surface. Toward this goal, we develop tools in the free group setting that mirror those for surface groups as well as discuss various analogs of subsurface projection; these may be of independent interest.