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arXiv · 1101.3798

Operations in the homology spectral sequence of a cosimplicial infinite loop space

Philip Hackney
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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 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. In the sequel we show that they agree with the usual Araki-Kudo operations on the abutment H_*(Tot X).

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Philip Hackney. 2011-01-19. Operations in the homology spectral sequence of a cosimplicial infinite loop space. https://doi.org/10.1016/j.jpaa.2012.10.002

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