Projection complexes and quasimedian maps

Mark F Hagen, Harry Petyt

Research output: Contribution to journalArticle (Academic Journal)peer-review


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.
Original languageEnglish
JournalAlgebraic and Geometric Topology
Publication statusAccepted/In press - 29 Aug 2021


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