Homology operations and cosimplicial iterated loop spaces

If X is a cosimplical E_{n+1} space then \operatorname{Tot}(X) is an E_{n+1} space and its mod 2 homology H_*(\operatorname{Tot}(X)) has Dyer-Lashof and Browder operations. It's natural to ask if the spectral sequence converging to H_*(\operatorname{Tot}(X)) admits compatible operations. In thi...

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Bibliographic Details
Published inHomology, homotopy, and applications Vol. 16; no. 1; pp. 1 - 25
Main Author Hackney, Philip
Format Journal Article
LanguageEnglish
Published International Press of Boston 2014
Subjects
55S12
55T20
Araki-Kudo operation
Browder operation
cosimplicial space
Dyer-Lashof operation
spectral sequence
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Summary:If X is a cosimplical E_{n+1} space then \operatorname{Tot}(X) is an E_{n+1} space and its mod 2 homology H_*(\operatorname{Tot}(X)) has Dyer-Lashof and Browder operations. It's natural to ask if the spectral sequence converging to H_*(\operatorname{Tot}(X)) admits compatible operations. In this paper we give a positive answer to this question.
ISSN:1532-0073
1532-0081
DOI:10.4310/HHA.2014.v16.n1.a1