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Higher order track categories and the algebra of higher order cohomology operations
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Hans-Joachim Baues
Veröffentlicht/Copyright:
19. März 2010
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.
Keywords.: Higher cohomology operations; higher homotopies; higher track categories; higher Toda brackets; higher Massey products; Adams spectral sequence; higher chain complexes
Received: 2009-10-13
Published Online: 2010-03-19
Published in Print: 2010-March
© de Gruyter 2010
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Artikel in diesem Heft
- A finite dimensional 𝐴∞ algebra example
- Cartan's constructions and the twisted Eilenberg–Zilber theorem
- Higher order track categories and the algebra of higher order cohomology operations
- A case study of 𝐴∞-structure
- Props in model categories and homotopy invariance of structures
- On the construction of 𝐴∞-structures
- A twisted tale of cochains and connections
Schlagwörter für diesen Artikel
Higher cohomology operations;
higher homotopies;
higher track categories;
higher Toda brackets;
higher Massey products;
Adams spectral sequence;
higher chain complexes
Artikel in diesem Heft
- A finite dimensional 𝐴∞ algebra example
- Cartan's constructions and the twisted Eilenberg–Zilber theorem
- Higher order track categories and the algebra of higher order cohomology operations
- A case study of 𝐴∞-structure
- Props in model categories and homotopy invariance of structures
- On the construction of 𝐴∞-structures
- A twisted tale of cochains and connections
