Subcomplexes on filtered manifolds

In this paper, we present a general construction of complexes on filtered manifolds. In the particular case of regular subRiemannian manifolds, we show that this yields the so-called Rumin complex when the manifold is also equipped with a compatible Riemannian metric. Another instance is set on a nilpotent Lie group equipped with a left invariant filtration; our scheme then computes the Lie algebra cohomology.