  A JSJ decomposition of a group is a splitting that allows one to classify all
possible splittings of the group over a certain family of edge groups. Although
JSJ decompositions are not unique in general, Guirardel--Levitt have
constructed a canonical JSJ decomposition, the tree of cylinders, which
classifies splittings of relatively hyperbolic groups over elementary
subgroups.
  In this paper, we give a new topological construction of the
Guirardel--Levitt tree of cylinders, and we show that this tree depends only on
the homeomorphism type of the Bowditch boundary. Furthermore, the tree of
cylinders admits a natural action by the group of homeomorphisms of the
boundary. In particular, the quasi-isometry group of $(G,\mathbb{P})$ acts
naturally on the tree of cylinders.
