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Commensurability of groups quasi-isometric to RAAG's

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NPCW01 - Non-positive curvature in action

It is well-known that a finitely generated group quasi-isometric to a free group is commensurable to a free group. We seek higher-dimensional generalization of this fact in the class of right-angled Artin groups (RAAG). Let G be a RAAG with finite outer automorphism group. Suppose in addition that the defining graph of G is star-rigid and has no induced 4-cycle. Then we show every finitely generated group quasi-isometric to G is commensurable to G. However, if the defining graph of G contains an induced 4-cycle, then there always exists a group quasi-isometric to G, but not commensurable to G. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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