Quasi-isometry classification of right-angled Artin group with finite outer automorphism group

Jingyin Huang (NYU)

Abstract: Let G_{1} and G_{2} be two right-angled Artin groups (RAAG) with finite outer automorphism group, we show they are quasi-isometric if and only if they are isomorphic. This is an extension of a previous result of Bestvina, Kleiner and Sageev about atomic groups. Moreover, given an RAAG G such that Out(G) is finite and another RAAG G' quasi-isometric to G, we show G' can be realized as a finite index subgroup in G.