Sobolev mappings and the Rumin complex

We consider contact manifolds equipped with CarnotCaratheodory 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 J ∗ ⊂ Ω∗G of the de Rham complex. Both results are applications of the Pullback Theorem from our previous paper.