EilenbergMacLane mapping algebras and higher distributivity up to homotopy
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 $2$distributivity, we provide a new construction of a derivation of degree $2$ of the mod $2$ Steenrod algebra.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 arXiv:
 arXiv:1703.07512
 Bibcode:
 2017arXiv170307512B
 Keywords:

 Mathematics  Algebraic Topology;
 55S20 (Primary) 55P20;
 55S10;
 18G55 (Secondary)
 EPrint:
 v3: Minor changes. Final version