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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