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Commensurability of groups quasi-isometric to RAAG's

Presented by: 
Jingyin Huang
Wednesday 11th January 2017 - 09:00 to 10:00
INI Seminar Room 1
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. 
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons