On the spectral sequence associated to a multicomplex

TL;DR

This paper explores the spectral sequence linked to multicomplexes, providing explicit formulas for all differentials, which enhances understanding of their algebraic structure.

Contribution

It introduces explicit formulas for differentials in the spectral sequence of a multicomplex, advancing computational techniques in homological algebra.

Findings

Explicit formulas for all differentials in the spectral sequence

Improved computational methods for multicomplexes

Enhanced understanding of the algebraic structure of multicomplex spectral sequences

Abstract

A multicomplex, also known as a twisted chain complex, has an associated spectral sequence via a filtration of its total complex. We give explicit formulas for all the differentials in this spectral sequence.