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Right-angled Coxeter groups commensurable to right-angled Artin groups

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No logo availableCentre International de Rencontres Mathématiques (CIRM)
 Levcovitz, Ivan

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Right-angled Coxeter groups commensurable to right-angled Artin groups
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A well-known result of Davis-Januszkiewicz is that every right-angled Artin group (RAAG) is commensurable to some rightangled Coxeter group (RACG). In this talk we consider the converse question: which RACGs are commensurable to some RAAG? To do so, we investigate some natural candidate RAAG subgroups of RACGs and characterize when such subgroups are indeed RAAGs. As an application, we show that a 2-dimensional, one-ended RACG with planar defining graph is quasiisometric to a RAAG if and only if it is commensurable to a RAAG. This talk is based on work joint with Pallavi Dani.