Homology operations and cosimplicial iterated loop spaces

Philip Hackney

doi:10.4310/HHA.2014.v16.n1.a1

Homology operations and cosimplicial iterated loop spaces

Philip Hackney^*

^*Corresponding author for this work

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

Abstract

If X is a cosimplical En+1 space then Tot(X) is an En+1 space and its mod 2 homology H-*(Tot(X)) has Dyer-Lashof and Browder operations. It's natural to ask if the spectral sequence converging to H-*(Tot(X)) admits compatible operations. In this paper we give a positive answer to this question.

Original language	English
Pages (from-to)	1-25
Number of pages	25
Journal	Homology, Homotopy and Applications
Volume	16
Issue number	1
DOIs	https://doi.org/10.4310/HHA.2014.v16.n1.a1
Publication status	Published - 2014
Externally published	Yes

Keywords

Araki-Kudo operation
Browder operation
Dyer-Lashof operation
cosimplicial space
spectral sequence
MOORE SPECTRAL SEQUENCE
Dyer-lashof operation
Cosimplicial space
Spectral sequence

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AB - If X is a cosimplical En+1 space then Tot(X) is an En+1 space and its mod 2 homology H-*(Tot(X)) has Dyer-Lashof and Browder operations. It's natural to ask if the spectral sequence converging to H-*(Tot(X)) admits compatible operations. In this paper we give a positive answer to this question.

KW - Araki-Kudo operation

KW - Browder operation

KW - Dyer-Lashof operation

KW - cosimplicial space

KW - spectral sequence

KW - MOORE SPECTRAL SEQUENCE

KW - Dyer-lashof operation

KW - Cosimplicial space

KW - Spectral sequence

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DO - 10.4310/HHA.2014.v16.n1.a1

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EP - 25

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

IS - 1

ER -

Homology operations and cosimplicial iterated loop spaces

Abstract

Keywords

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