Spectral complexes from truncated multicomplexes

TL;DR

This paper introduces spectral complexes derived from truncated multicomplexes, inspired by spectral sequences, which refine the Rumin complex and preserve cohomology, aiding subRiemannian geometry studies.

Contribution

It presents a novel construction of spectral complexes from truncated multicomplexes that align with spectral sequence differentials and refine existing complexes.

Findings

Constructed spectral complexes that coincide with spectral sequence differentials.

Refined the Rumin complex while preserving cohomology.

Provided new tools for subRiemannian geometry analysis.

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.