2021/08/30 by Hagen, Mark, Petyt, Harry · 1 citation
#FOS: Mathematics #Group Theory (math.GR) #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.2108.13232
We use the projection complex machinery of Bestvina--Bromberg--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.