Operations in the homology spectral sequence of a cosimplicial infinite loop space
arXiv:1101.3798 · doi:10.1016/j.jpaa.2012.10.002
Abstract
Consider the mod 2 homology spectral sequence associated to a cosimplicial space X. We construct external operations whose target is the spectral sequence associated to EΣ_2 \times_{Σ_2} (X\times X). If X is a cosimplicial E_\infty-space, we couple these external operations with the structure map EΣ_2 \times_{Σ_2} (X\times X) \to X to produce internal operations in the spectral sequence. In the sequel we show that they agree with the usual Araki-Kudo operations on the abutment H_*(Tot X).
final version