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.
Fields of Study & Subjects
Geometric and Algebraic Topology
Cellular Automata and Applications
semigroups and automata theory
Publication details
- Journal / source
- Pacific Journal of Mathematics
- Volume
- 341
- Issue
- 2
- Pages
- 305–377
- Publication date
- 23 March 2026
- Language
- EN