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Higher order track categories and the algebra of higher order cohomology operations

Higher order track categories and the algebra of higher order cohomology operations We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an 𝑛-th order track category suitable for studying higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also, differential algebras give rise to higher order track categories. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Higher order track categories and the algebra of higher order cohomology operations

Georgian Mathematical Journal , Volume 17 (1) – Mar 1, 2010

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References (12)

Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2010.002
Publisher site
See Article on Publisher Site

Abstract

We describe a conjecture on the algebra of higher cohomology operations which leads to the computations of the differentials in the Adams spectral sequence. For this we introduce the notion of an 𝑛-th order track category suitable for studying higher order Toda brackets and the differentials in spectral sequences. We describe various examples of higher order track categories which are topological, in particular the track category of higher cohomology operations. Also, differential algebras give rise to higher order track categories.

Journal

Georgian Mathematical Journalde Gruyter

Published: Mar 1, 2010

Keywords: Higher cohomology operations; higher homotopies; higher track categories; higher Toda brackets; higher Massey products; Adams spectral sequence; higher chain complexes

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