The Rumin complex on nilpotent Lie groups

In this paper an alternative definition of the Rumin complex $(E_0^\bullet,d_c)$ is presented, one that relies on a different concept of weights of forms. In this way, the Rumin complex can be constructed on any nilpotent Lie group equipped with a Carnot-Carath\'eodory metric. Moreover, this construction allows for the direct application of previous non-vanishing results of $\ell^{q,p}$ cohomology to all nilpotent Lie groups that admit a positive grading.