Abstract
We use the projection complex machinery of Bestvina, Bromberg, and Fujiwara to study hierarchically hyperbolic groups. In particular, we show that if the group has a BBF colouring and its associated hyperbolic spaces are quasiisometric to trees, then the group is quasiisometric to a finite-dimensional CAT(0) cube complex. We deduce various properties, including the Helly property for hierarchically quasiconvex subsets.
Citation
Mark F Hagen. Harry Petyt. "Projection complexes and quasimedian maps." Algebr. Geom. Topol. 22 (7) 3277 - 3304, 2022. https://doi.org/10.2140/agt.2022.22.3277
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