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Journal of Homotopy and Related Structures

, Volume 11, Issue 4, pp 679–713 | Cite as

2-track algebras and the Adams spectral sequence

  • Hans-Joachim Baues
  • Martin FranklandEmail author
Article
  • 57 Downloads

Abstract

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.

Keywords

Adams spectral sequence Tertiary Toda bracket 2-track groupoid Bigroupoid Double groupoid 

Mathematics Subject Classification

55T15 18G50 55S20 

Notes

Acknowledgements

We thank the referee for their helpful comments. The second author thanks the Max-Planck-Institut für Mathematik Bonn for its generous hospitality, as well as David Blanc, Robert Bruner, Dan Christensen, and Dan Isaksen for useful conversations.

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Copyright information

© Tbilisi Centre for Mathematical Sciences 2016

Authors and Affiliations

  1. 1.Max-Planck-Institut für MathematikBonnGermany
  2. 2.Institut für MathematikUniversität OsnabrückOsnabrückGermany

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