The Rumin complex on nilpotent Lie groups

Abstract

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-Carathéodory 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.