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A combinatorial
structure for many hierarchically hyperbolic spaces
Mark Hagen, Giorgio Mangioni and Alessandro Sisto |
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Vol. 341 (2026), No. 2, 305–377
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Abstract |
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The combinatorial hierarchical hyperbolicity criterion is a very useful way of constructing new hierarchically hyperbolic spaces (HHSs). We show that, conversely, HHSs satisfying natural assumptions (satisfied, for example, by mapping class groups) admit a combinatorial HHS structure. This can be useful in constructions of new HHSs, and also our construction clarifies how to apply the combinatorial HHS criterion to suspected examples. We also uncover connections between HHS notions and lattice theory notions. |
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This has nothing to do with links. – A. S. |
Keywords
hierarchical hyperbolicity, combinatorial HHS
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Mathematical Subject Classification
Primary: 20F65
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Milestones
Received: 13 September 2023
Revised: 15 January 2026
Accepted: 15 January 2026
Published: 23 March 2026
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Authors |
| Mark Hagen | |
| School of Mathematics University of Bristol Bristol United Kingdom |
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| Giorgio Mangioni | |
| Maxwell Institute and Department of
Mathematics Heriot-Watt University Edinburgh United Kingdom |
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| Alessandro Sisto | |
| Maxwell Institute and Department of
Mathematics Heriot-Watt University Edinburgh United Kingdom |
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| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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