A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces
Group Theory
2026-03-25 v2 Geometric Topology
Metric Geometry
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.
Cite
@article{arxiv.2308.16335,
title = {A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces},
author = {Mark Hagen and Giorgio Mangioni and Alessandro Sisto},
journal= {arXiv preprint arXiv:2308.16335},
year = {2026}
}
Comments
66 pages, 10 figures. To appear in Pacific J. Math