2-track algebras and the Adams spectral sequence

Autor(en): Baues, Hans-Joachim
Frankland, Martin
Stichwörter: 2-track groupoid; Adams spectral sequence; Bigroupoid; CATEGORIES; Double groupoid; FUNCTORS; Mathematics; Tertiary; Toda bracket
Erscheinungsdatum: 2016
Herausgeber: SPRINGER HEIDELBERG
Journal: JOURNAL OF HOMOTOPY AND RELATED STRUCTURES
Volumen: 11
Ausgabe: 4, SI
Startseite: 679
Seitenende: 713
Zusammenfassung: 
In previous work of the first author and Jibladze, the E-3-term of the Adams spectral sequence was described as a secondary derived functor, defined via secondary chain complexes in a groupoid-enriched category. This led to computations of the E-3-term using the algebra of secondary cohomology operations. In work with Blanc, an analogous description was provided for all higher terms E-r. In this paper, we introduce 2-track algebras and tertiary chain complexes, and we show that the E-4-term of the Adams spectral sequence is a tertiary Ext group in this sense. This extends the work with Jibladze, while specializing the work with Blanc in a way that should be more amenable to computations.
ISSN: 21938407
DOI: 10.1007/s40062-016-0147-x

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