Paper detail

The geometry of purely loxodromic subgroups of right-angled Artin groups

We prove that finitely generated purely loxodromic subgroups of a right-angled Artin group $A(Γ)$ fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups $\text{Mod}(S)$. In particular, such subgroups are quasiconvex in $A(Γ)$. In addition, we identify a milder condition for a finitely generated subgroup of $A(Γ)$ that guarantees it is free, undistorted, and retains finite generation when intersected with $A(Λ)$ for subgraphs $Λ$ of $Γ$. These results have applications to both the study of convex cocompactness in $\text{Mod}(S)$ and the way in which certain groups can embed in right-angled Artin groups.