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.
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