Multicomplexes on Carnot groups and their associated spectral sequence

TL;DR

This paper explores the connection between the Rumin complex and spectral sequences on Carnot groups, providing insights into their cohomological properties through a detailed analysis of filtered forms.

Contribution

It introduces a comprehensive study of the spectral sequence derived from the Rumin complex on Carnot groups, highlighting new relationships with de Rham cohomology.

Findings

Established a link between the Rumin complex and spectral sequences on Carnot groups.

Provided computations of the spectral sequence for specific classes of Carnot groups.

Enhanced understanding of the cohomological structure of Carnot groups.

Abstract

The aim of this paper is to give a thorough insight into the relationship between the Rumin complex on Carnot groups and the spectral sequence obtained from the filtration on forms by homogeneous weights that computes the de Rham cohomology of the underlying group.