Abstract
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.
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.
| Original language | English |
|---|---|
| Journal | Algebraic and Geometric Topology |
| Publication status | Accepted/In press - 29 Aug 2021 |