Minimal cubings
  We combine ideas of Scott and Swarup on good position for almost invariant subsets of a group with ideas of Sageev on constructing cubings from such sets. We construct cubings which are more canonical than in Sageev's original construction. We also show that almost invariant sets can be chosen to be in very good position. 
Graham Niblo, Michah Sageev, Peter Scott, Gadde A. Swarup