Homology operations and cosimplicial iterated loop spaces

Details Homology operations and cosimplicial iterated loop spaces Homology operations and cosimplicial iterated loop spaces

2011-01-31

arxiv.org/abs/1102.0020v1

Mathematics

Algebraic Topology

Scientific paper

The mod 2 homology spectral sequence associated to a cosimplicial E_{n+1}-space admits homology operations. We prove this by constructing, for any cosimplicial space X, external operations (including a Browder operation) landing in the spectral sequence associated to S^n \times_{\Sigma_2} (X\times X). When X is a cosimplicial E_{n+1}-space we couple the external operations with the levelwise structure maps to produce internal operations in the spectral sequence. Bousfield identified H_*(Tot X) as the target of this spectral sequence. Noting that Tot X is an E_{n+1}-space when X is a cosimplicial E_{n+1}-space, we show that the operations constructed above agree with the usual Araki-Kudo and Browder operations in the target.

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