Homology operations and cosimplicial infinite loop spaces. I

Details Homology operations and cosimplicial infinite loop spaces. I Homology operations and cosimplicial infinite loop spaces. I

2011-01-19

arxiv.org/abs/1101.3798v2

Mathematics

Algebraic Topology

v2: Submitted version. Changes are extremely minor: added "I" to the title, modified references to subsequent papers in the se

Scientific paper

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 E\Sigma_2 \times_{\Sigma_2} (X\times X). If X is a cosimplicial E_\infty-space, we couple these external operations with the structure map E\Sigma_2 \times_{\Sigma_2} (X\times X) \to X to produce internal operations in the spectral sequence. We do not know if these agree with the operations previously constructed by Jim Turner in this situation, but in the sequel we show that they agree with the usual Araki-Kudo operations on the abutment H_*(Tot X).

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