English

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

Algebraic Topology 2013-09-10 v3

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).

Keywords

Cite

@article{arxiv.1101.3798,
  title  = {Operations in the homology spectral sequence of a cosimplicial infinite loop space},
  author = {Philip Hackney},
  journal= {arXiv preprint arXiv:1101.3798},
  year   = {2013}
}

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