Projection complexes and quasimedian maps

Hagen, Mark F; Petyt, Harry

doi:10.2140/agt.2022.22.3277

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Projection complexes and quasimedian maps

Mark F Hagen and Harry Petyt

Algebraic & Geometric Topology 22 (2022) 3277–3304

DOI: 10.2140/agt.2022.22.3277

Abstract

We use the projection complex machinery of Bestvina, Bromberg, and 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

projection complexes, hierarchical hyperbolicity, quasitrees, quasiisometries, CAT(0) cube complexes

Mathematical Subject Classification 2010

Primary: 20F65, 20F67

References

Publication

Received: 31 October 2019

Revised: 2 August 2021

Accepted: 28 August 2021

Published: 30 January 2023

Authors

Mark F Hagen
School of Mathematics University of Bristol Bristol United Kingdom

Harry Petyt
School of Mathematics University of Bristol Bristol United Kingdom

Volume 22, issue 7 (2022)