 

HansJoachim Baues and Martin Frankland
EilenbergMacLane mapping algebras and higher distributivity up to homotopy view print


Published: 
October 26, 2017 
Keywords: 
Higher distributivity, distributivity up to homotopy, higher cohomology operation, EilenbergMacLane spectrum, Steenrod algebra, Kristensen derivation, homotopy invariant, Ainfinity morphism, topological abelian group, mapping theory, mapping algebra 
Subject: 
Primary: 55S20; Secondary: 55P20, 55S10, 18G55 


Abstract
Primary cohomology operations, i.e., elements of the Steenrod algebra, are given by homotopy classes of maps between EilenbergMacLane spectra. Such maps (before taking homotopy classes) form the topological version of the Steenrod algebra. Composition of such maps is strictly linear in one variable and linear up to coherent homotopy in the other variable. To describe this structure, we introduce a hierarchy of higher distributivity laws, and prove that the topological Steenrod algebra satisfies all of them. We show that the higher distributivity laws are homotopy invariant in a suitable sense. As an application of 2distributivity, we provide a new construction of a
derivation of degree 2 of the mod 2 Steenrod algebra.


Acknowledgements
The second author was partially funded by a grant of the DFG SPP 1786: Homotopy Theory and Algebraic Geometry


Author information
HansJoachim Baues:
MaxPlanckInstitut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
baues@mpimbonn.mpg.de
Martin Frankland:
Universität Osnabrück, Institut für Mathematik, Albrechtstr. 28a, 49076 Osnabrück, Germany
martin.frankland@uniosnabrueck.de

