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

2009/03/16 by Hans-Joachim Baues, Baues, Hans-Joachim
Mathematics · Physics and Astronomy · #(55U99 #18G10 #18G25 #18G40) #18O05 #55S20 #55T15 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.0903.2876

openalex publication_date 2009/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 which is suitable to study 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.

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