A combinatorial structure for many hierarchically hyperbolic spaces

Mark Hagen; Giorgio Mangioni; Alessandro Sisto

doi:10.2140/pjm.2026.341.305

A combinatorial structure for many hierarchically hyperbolic spaces

Mark Hagen
, Giorgio Mangioni
, Alessandro Sisto

Research output: Contribution to journal › Article › peer-review

6 Downloads (Pure)

Abstract

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.

Original language	English
Pages (from-to)	305-377
Number of pages	73
Journal	Pacific Journal of Mathematics
Volume	341
Issue number	2
Early online date	23 Mar 2026
DOIs	https://doi.org/10.2140/pjm.2026.341.305
Publication status	Published - Apr 2026

Keywords

combinatorial HHS
hierarchical hyperbolicity

ASJC Scopus subject areas

General Mathematics

Access to Document

10.2140/pjm.2026.341.305Licence: CC BY

Download pdf
© 2026 The Author(s).
Final published version, 776 KBLicence: CC BY

Cite this

@article{2a976534afc049e6977a42c6a1522fa9,

title = "A combinatorial structure for many hierarchically hyperbolic spaces",

abstract = "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.",

keywords = "combinatorial HHS, hierarchical hyperbolicity",

author = "Mark Hagen and Giorgio Mangioni and Alessandro Sisto",

note = "Publisher Copyright: {\textcopyright} 2026 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.",

year = "2026",

month = apr,

doi = "10.2140/pjm.2026.341.305",

language = "English",

volume = "341",

pages = "305--377",

journal = "Pacific Journal of Mathematics",

issn = "0030-8730",

publisher = "Mathematical Sciences Publishers",

number = "2",

}

TY - JOUR

T1 - A combinatorial structure for many hierarchically hyperbolic spaces

AU - Hagen, Mark

AU - Mangioni, Giorgio

AU - Sisto, Alessandro

N1 - Publisher Copyright: © 2026 The Authors, under license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). Open Access made possible by subscribing institutions via Subscribe to Open.

PY - 2026/4

Y1 - 2026/4

N2 - 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.

AB - 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.

KW - combinatorial HHS

KW - hierarchical hyperbolicity

UR - https://www.scopus.com/pages/publications/105037831147

U2 - 10.2140/pjm.2026.341.305

DO - 10.2140/pjm.2026.341.305

M3 - Article

AN - SCOPUS:105037831147

SN - 0030-8730

VL - 341

SP - 305

EP - 377

JO - Pacific Journal of Mathematics

JF - Pacific Journal of Mathematics

IS - 2

ER -

A combinatorial structure for many hierarchically hyperbolic spaces

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this