  We consider contact manifolds equipped with Carnot-Caratheodory metrics, and
show that the Rumin complex is respected by Sobolev mappings: Pansu pullback
induces a chain mapping between the smooth Rumin complex and the distributional
Rumin complex. As a consequence, the Rumin flat complex -- the analog of the
Whitney flat complex in the setting of contact manifolds -- is bilipschitz
invariant.
  We also show that for Sobolev mappings between general Carnot groups, Pansu
pullback induces a chain mapping when restricted to a certain differential
ideal of the de Rham complex.
  Both results are applications of the Pullback Theorem from our previous
paper.
