  Inspired by Rumin's work on a subcomplex in sub-Riemannian manifolds which is
cohomologically equivalent to the de Rham complex, we present a more general
construction that produces subcomplexes from any filtered cochain complex of
finite depth and still computes the cohomology of the original filtered
complex. A priori these subcomplexes depend not only on the filtration itself,
but also on the choice of additional structures. However, we show that the
construction only depends on the given filtration up to isomorphism. Finally,
we show how such subcomplexes relate to spectral sequences, a cohomological
machinery that arises naturally when considering a filtered complex.

Differential Geometry;Algebraic Topology