Scott and Swarup's regular neighbourhood as a tree of cylinders
  Let G be a finitely presented group. Scott and Swarup have constructed a canonical splitting of G which encloses all almost invariant sets over virtually polycyclic subgroups of a given length. We give an alternative construction of this regular neighbourhood, by showing that it is the tree of cylinders of a JSJ splitting. 
Vincent Guirardel, Gilbert Levitt