Spectral sequence operations converge to Araki-Kudo operations

Philip Hackney

doi:10.1016/j.jpaa.2012.12.001

Spectral sequence operations converge to Araki-Kudo operations

Philip Hackney^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

Previously, we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E-infinity-space X. The correct target for this spectral sequence is the homology of Tot X. Noting that in this setting Tot X is an E-infinity-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). (C) 2012 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	1716-1739
Number of pages	24
Journal	Journal of Pure and Applied Algebra
Volume	217
Issue number	9
DOIs	https://doi.org/10.1016/j.jpaa.2012.12.001
Publication status	Published - Sep 2013
Externally published	Yes

Access to Document

10.1016/j.jpaa.2012.12.001

Cite this

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title = "Spectral sequence operations converge to Araki-Kudo operations",

abstract = "Previously, we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E-infinity-space X. The correct target for this spectral sequence is the homology of Tot X. Noting that in this setting Tot X is an E-infinity-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). (C) 2012 Elsevier B.V. All rights reserved.",

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AB - Previously, we constructed operations in the mod 2 homology spectral sequence associated to a cosimplicial E-infinity-space X. The correct target for this spectral sequence is the homology of Tot X. Noting that in this setting Tot X is an E-infinity-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). (C) 2012 Elsevier B.V. All rights reserved.

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DO - 10.1016/j.jpaa.2012.12.001

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