# Hierarchically hyperbolic spaces II: Combination theorems and the distance formula

@article{Behrstock2019HierarchicallyHS, title={Hierarchically hyperbolic spaces II: Combination theorems and the distance formula}, author={Jason A. Behrstock and Mark F. Hagen and Alessandro Sisto}, journal={Pacific Journal of Mathematics}, year={2019} }

We introduce a number of tools for finding and studying \emph{hierarchically hyperbolic spaces (HHS)}, a rich class of spaces including mapping class groups of surfaces, Teichmuller space with either the Teichmuller or Weil-Petersson metrics, right-angled Artin groups, and the universal cover of any compact special cube complex. We begin by introducing a streamlined set of axioms defining an HHS. We prove that all HHSs satisfy a Masur-Minsky-style distance formula, thereby obtaining a new proof…

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