Stallings folds for CAT(0) cube complexes and quasiconvex subgroups
  We describe a higher dimensional analogue of the Stallings folding sequence for group actions on CAT(0) cube complexes. We use it to give a characterization of quasiconvex subgroups of hyperbolic groups which act properly co-compactly on CAT(0) cube complexes via finiteness properties of their hyperplane stabilizers. 
Benjamin Beeker and Nir Lazarovich
math.GR