Homology operations and cosimplicial infinite loop spaces. II

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

2011-01-27

arxiv.org/abs/1101.5395v2

Mathematics

Algebraic Topology

v2: Submitted version. Minor changes: renamed a couple of maps, shortened proof of proposition 7.1, different style, added arx

Scientific paper

Previously we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E_\infty-space X. According to Bousfield, the correct target for this spectral sequence is the homology of Tot X. Noting that in this setting Tot X is an E_\infty-space, we show that our operations agree with the usual Araki-Kudo operations in the target. We also prove that the multiplication in the spectral sequence agrees with the multiplication in H_*(Tot X).

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