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Hierarchical hyperbolicity of graphs of multicurves

Kate M Vokes

Algebraic & Geometric Topology 22 (2022) 113–151

We show that many graphs naturally associated to a connected, compact, oriented 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.

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curve complex, curve graph, mapping class group, hierarchical hyperbolicity
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57M99
Received: 2 August 2019
Revised: 25 January 2021
Accepted: 5 March 2021
Published: 26 April 2022
Kate M Vokes
Institut des Hautes Études Scientifiques