A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces

Mark Hagen; Giorgio Mangioni; Alessandro Sisto

doi:10.48550/arXiv.2308.16335

A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces

Mark Hagen, Giorgio Mangioni, Alessandro Sisto

School of Mathematics

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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
DOIs	https://doi.org/10.48550/arXiv.2308.16335
Publication status	Submitted - 30 Aug 2023

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64 pages, 10 figures

Keywords

math.GR
math.GT
math.MG

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A Combinatorial Structure for Many Hierarchically Hyperbolic Spaces

Abstract

Bibliographical note

Keywords

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