Relative Hyperbolicity and Artin Groups

Let G=⟨ a1,&ldots; , an | aiajai&ldots; = a_ja_ia_j,&ldots; ,i>j⟩ be an Artin group and let mij =mji be the length of each of the sides of the defining relation involving aiand aj. We show if all m_ij ⩾ 7 then G is relatively hyperbolic in the sense of Farb with respect to the collection of its two-generator subgroups 〈ai, aj〉for which m_ij >&infty;.