English

Projection complexes and quasimedian maps

Group Theory 2021-08-31 v1 Metric Geometry

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.

Keywords

Cite

@article{arxiv.2108.13232,
  title  = {Projection complexes and quasimedian maps},
  author = {Mark Hagen and Harry Petyt},
  journal= {arXiv preprint arXiv:2108.13232},
  year   = {2021}
}

Comments

18 pages, to appear in Algebr. Geom. Topol

R2 v1 2026-06-24T05:31:45.441Z