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A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces

Authors :
Hagen, Mark
Mangioni, Giorgio
Sisto, Alessandro
Publication Year :
2023

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.<br />Comment: 64 pages, 10 figures

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2308.16335
Document Type :
Working Paper