Spectral complexes from truncated multicomplexes

Abstract

This paper introduces a new construction of subcomplexes associated with a truncated multicomplex. Inspired by the machinery of spectral sequences, this construction yields a collection of interrelated subcomplexes whose differentials coincide with the spectral sequence differentials. These complexes refine the Rumin complex and retain the cohomology of the underlying multicomplex, providing a new tool for the study of subRiemannian geometry, particularly on Carnot groups.