Homology, Homotopy and Applications

Homology operations and cosimplicial iterated loop spaces

Philip Hackney

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Abstract

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.

Article information

Source
Homology Homotopy Appl., Volume 16, Number 1 (2014), 1-25.

Dates
First available in Project Euclid: 3 June 2014

Permanent link to this document
https://projecteuclid.org/euclid.hha/1401800069

Mathematical Reviews number (MathSciNet)
MR3171258

Zentralblatt MATH identifier
1295.55016

Subjects
Primary: 55S12: Dyer-Lashof operations 55T20: Eilenberg-Moore spectral sequences [See also 57T35]

Keywords
Araki-Kudo operation Browder operation Dyer-Lashof operation cosimplicial space spectral sequence

Citation

Hackney, Philip. Homology operations and cosimplicial iterated loop spaces. Homology Homotopy Appl. 16 (2014), no. 1, 1--25. https://projecteuclid.org/euclid.hha/1401800069


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