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Projection complexes
and quasimedian maps
Mark F Hagen and Harry Petyt |
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Algebraic & Geometric Topology 22 (2022) 3277–3304
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Abstract |
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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. |
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Keywords
projection complexes, hierarchical hyperbolicity,
quasitrees, quasiisometries, CAT(0) cube complexes
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Mathematical Subject Classification 2010
Primary: 20F65, 20F67
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References |
Publication
Received: 31 October 2019
Revised: 2 August 2021
Accepted: 28 August 2021
Published: 30 January 2023
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Authors |
| Mark F Hagen | |
| School of Mathematics University of Bristol Bristol United Kingdom |
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| Harry Petyt | |
| School of Mathematics University of Bristol Bristol United Kingdom |
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