Embedability of right-angled Artin groups into hierarchically hyperbolic groups
Abstract
For a hierarchically hyperbolic group, we provide sufficient conditions under which suitable powers of a finite collection of elements generate a right-angled Artin subgroup. Under additional hypotheses, we further show that this subgroup can be promoted to be quasi-isometrically embedded. Our framework recovers and unifies earlier results, including those of Clay-Leininger-Mangahas CLM12 and Runnels Run21 for mapping class groups, and of Kim-Koberda KK13 for right-angled Artin groups.
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