2021/07/05 by Benjamin Matschke, Matschke, Benjamin
Biochemistry, Genetics and Molecular Biology · Mathematics · #55T05 (Primary) 55T10 #55T15 #55T20 #55T25 (Secondary) #55U20 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Protein Tyrosine Phosphatases #math.AT #msc:55T05 #msc:55T10 #msc:55T15 #msc:55T20 #msc:55T25 #msc:55U20
paper · pdf · doi:10.48550/arxiv.2107.02130
13 pages, 3 figures, improved presentation, added examples
openalex publication_date 2021/07/05 · arxiv created 2021/07/06 · arxiv updated 2021/07/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.