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

Philip Hackney

doi:10.1016/j.jpaa.2012.10.002

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

Philip Hackney^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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) x (Sigma 2) (X x X). If X is a cosimplicial E-infinity-space, we couple these external operations with the structure map

E Sigma(2) x (Sigma 2)(X x X) -> 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). (C) 2012 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1350-1377
Number of pages	28
Journal	Journal of Pure and Applied Algebra
Volume	217
Issue number	7
DOIs	https://doi.org/10.1016/j.jpaa.2012.10.002
Publication status	Published - Jul 2013
Externally published	Yes

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title = "Operations in the homology spectral sequence of a cosimplicial infinite loop space",

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) x (Sigma 2) (X x X). If X is a cosimplicial E-infinity-space, we couple these external operations with the structure mapE Sigma(2) x (Sigma 2)(X x X) -> Xto 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). (C) 2012 Elsevier B.V. All rights reserved.",

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N2 - 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) x (Sigma 2) (X x X). If X is a cosimplicial E-infinity-space, we couple these external operations with the structure mapE Sigma(2) x (Sigma 2)(X x X) -> Xto 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). (C) 2012 Elsevier B.V. All rights reserved.

AB - 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) x (Sigma 2) (X x X). If X is a cosimplicial E-infinity-space, we couple these external operations with the structure mapE Sigma(2) x (Sigma 2)(X x X) -> Xto 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). (C) 2012 Elsevier B.V. All rights reserved.

U2 - 10.1016/j.jpaa.2012.10.002

DO - 10.1016/j.jpaa.2012.10.002

M3 - Article

SN - 0022-4049

VL - 217

SP - 1350

EP - 1377

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 7

ER -

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

Abstract

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