Higher spectral sequences

In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in \(n\) compatible ways. For this we extend the previous spectral system construction of the author, and we show that it admits considerably more differentials than wha...

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Bibliographic Details
Published in:arXiv.org 2021-07
Main Author: Matschke, Benjamin
Format: Article
Language:English
Subjects:
Spectra
Online Access:Get full text
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Summary:In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in \(n\) compatible ways. For this we extend the previous spectral system construction of the author, and we show that it admits considerably more differentials than what was previously known. As a result, this endows the successive Leray--Serre, Grothendieck, chromatic--Adams--Novikov, and Eilenberg--Moore spectral sequences of the author with the structure of a higher spectral sequence. Another application is a universal coefficient theorem analog for spectral sequences.
ISSN:2331-8422