Hierarchical hyperbolicity of graphs of multicurves

Vokes, Kate M

doi:10.2140/agt.2022.22.113

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Hierarchical hyperbolicity of graphs of multicurves

Kate M Vokes

Algebraic & Geometric Topology 22 (2022) 113–151

DOI: 10.2140/agt.2022.22.113

Abstract

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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Keywords

curve complex, curve graph, mapping class group, hierarchical hyperbolicity

Mathematical Subject Classification 2010

Primary: 20F65

Secondary: 57M99

References

Publication

Received: 2 August 2019

Revised: 25 January 2021

Accepted: 5 March 2021

Published: 26 April 2022

Authors

Kate M Vokes
Institut des Hautes Études Scientifiques Bures-sur-Yvette France
https://www.ihes.fr/~vokes

Volume 22, issue 1 (2022)