Hierarchically hyperbolic spaces I: curve complexes for cubical groups

@article{Behrstock2014HierarchicallyHS,
  title={Hierarchically hyperbolic spaces I: curve complexes for cubical groups},
  author={J. Behrstock and Mark F. Hagen and A. Sisto},
  journal={arXiv: Geometric Topology},
  year={2014}
}
In the context of CAT(0) cubical groups, we develop an analogue of the theory of curve complexes and subsurface projections. The role of the subsurfaces is played by a collection of convex subcomplexes called a \emph{factor system}, and the role of the curve graph is played by the \emph{contact graph}. There are a number of close parallels between the contact graph and the curve graph, including hyperbolicity, acylindricity of the action, the existence of hierarchy paths, and a Masur--Minsky… Expand

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