Hierarchical hyperbolicity of graphs of multicurves

Abstract

We show that many graphs naturally associated to a connected, compact, orientable surface are hierarchically hyperbolic spaces in the sense of Behrstock, Hagen and Sisto. They also automatically have the coarse median property defined by Bowditch. Consequences for such graphs include a distance formula analogous to Masur and Minsky's distance formula for the mapping class group, an upper bound on the maximal dimension of quasiflats, and the existence of a quadratic isoperimetric inequality. The hierarchically hyperbolic structure also gives rise to a simple criterion for when such graphs are Gromov hyperbolic.

27 pages, 4 figures. Minor changes from previous version. Addition of appendix describing a hierarchically hyperbolic structure on the arc graph

Cited by in corpus (5)

• Coarse injectivity, hierarchical hyperbolicity, and semihyperbolicity
• The (non)-relative hyperbolicity of the separating curve graph
• Extensions of multicurve stabilizers are hierarchically hyperbolic
• Curve graphs for Artin-Tits groups of type $B$, $\tilde{A}$ and $\tilde{C}$ are hyperbolic
• Asymptotic dimensions of the arc graphs and disk graphs