Multicomplexes and spectral sequences

TL;DR

This paper provides algebraic examples illustrating the differences between multicomplexes and their associated spectral sequences, motivated by applications in Morse-Bott homology.

Contribution

It introduces specific algebraic examples that highlight the distinction between multicomplexes and spectral sequences, advancing understanding in algebraic topology.

Findings

Examples show differentials in multicomplexes differ from those in spectral sequences.

Clarifies the algebraic structure underlying Morse-Bott homology.

Highlights the importance of algebraic distinctions in topological applications.

Abstract

In this note we present some algebraic examples of multicomplexes whose differentials differ from those in the spectral sequences associated to the multicomplexes. The motivation for constructing examples showing the algebraic distinction between a multicomplex and its associated spectral sequence comes from the author's work on Morse-Bott homology with A. Banyaga.